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I would challenge the assumption that the evils committed while a person is alive are finite.

Presumably, you are suggesting this because they took place during a finite period of time, or because human capability is finite. However, the duration of the evil is not the (only) way to determine the "magnitude" of the evil. If one reasonable definition of "evil" is "that which is not good", then the amount of evil would be related to how far away from good it is.

Under the Christian belief system, the standard of "good" is God; who is considered "infinitely good", or "perfect". Something which less than infinite is not finitely less than the infinite. In other words, the scale is not 1-10, where if you get a 2 it means that you were "level 8 evil; 8 short of perfect". Rather, the scale is 1-infinity, where getting a 2 means that you were infinitely evil. Even getting a 1,000,000 is still "infinitely evil".

This general reasoning is explained by J. Warner Wallace, along with a few other explanations, in this article on coldcasechristianity:

If someone embezzles $5.00 a week from their employer’s cash register they will have stolen $260.00 over the course of a year. If they’re caught at the end of this time, they would still only be guilty of a misdemeanor in the State of California (based on the total amount of loss). Although the crime took a year to commit, the perpetrator wouldn’t spend much (if any) time in jail. On the other hand, a murder can take place in the blink of an eye and the resulting punishment will be life in prison (or perhaps the death penalty). The duration of the crime clearly has little or nothing to do with the duration of the penalty.

And

Finally, it’s important to remember the nature of the crime that eventually leads one to Hell. It’s not the fact you kicked your dog in 1992. It’s not the fact you had evil thoughts about your teacher in 1983. The crime that earns us a place in Hell is our rejection of the true, living, eternal God. The rejection of God’s forgiveness is not finite. People who reject Jesus have rejected Him completely. They have rejected Him as an ultimate, final mortal decision. God has the right (and obligation) to judge them with an appropriate punishment. To argue that God’s punishment does not fit our crime is to underestimate our crime.

I can direct you to a quote that provides an answer, from the controversial theologian Thomas Altizer. He basically says that, in the round, the evil created in creation is extinguised in redemption -- signified by the crucifixion. However, there are subtleties as to what he means by 'in the round', i.e. predestination, or viewing the subject as a conceptual whole.

From Godhead and the Nothing, Chapter 5. Evil and the Godhead (page 65)

Why is there any being at all? Why far rather not nothing? This deep
question of Leibnitz was profoundly renewed in the twentieth century,
and asked as it never could have been asked in the seventeenth
century. This becomes perhaps the most ultimate question of Heidegger,
and is just as profoundly asked by Kafka or Beckett, and if this
question is now unanswerable, then so, too, is every ultimate
question. Of course, predestination can answer this question, but if
predestination has now become unthinkable, then so likewise have
Godhead and evil become unthinkable, and above all unthinkable if they
cannot be thought simultaneously and at once. Is it because we cannot
now think Godhead or totality without thinking evil that we so
resolutely refuse to think about God? ... Is damnation the necessarily
unspoken answer to our question as to why is there any being at all?
And if predestination knows the necessity of damnation, and the
absolute necessity of damnation, is that a damnation truly and finally
inseparable from the only redemption that predestination can know?
Here, if "being" is embodied in redemption, must "being" be embodied
in damnation as well?

Of course, it has now become impossible for us truly or actually to
speak of "being," but we have no less lost the capacity to speak of
either damnation or redemption. While this is certainly not true of
full modernity, it is apparently true of a new postmodernity, and
certainly true of a language in which the "I" or the center of
consciousness is silent and unspeakable. Nietzsche could know that "I"
as a pure negativity, an "I" that is the consequence of ressentiment,
but that knowledge is a dialectical knowledge, for it is the
consequence of the full advent of an absolute Yes-saying, a Yes-saying
which Nietzsche knew as redemption. Just as this "I" is a truly evil
"I," one that is the consequence of a pure No-saying, it is this very
"I" that is transfigured in an absolute Yes-saying, and transfigured
by undergoing an ultimate and final reversal, a reversal in which it
becomes the very opposite of itself.

As a member of the Church of Jesus Christ of Latter-day Saints the view is different.

God is Just. Satan's greatest lie is that you can get away with something. God is absolutely just and you will pay back everyone you hurt in this life and will be accountable for every action and every thought.

Jesus and the atonement brings mercy for those who sincerely seek it and have done everything in their power to make things right. Christ and his atonement cleans up all the residual (good not done and ripples that spread out throughout mankind from each wrong act).

Hell is each person paying back those they hurt. And the consequences of ignoring their conscience (God's voice in your soul) in this life.

As in the book, "Heaven and Hell" by EMANUEL SWEDENBORG 1700s (not LDS) the top heaven is for those who love God (the $500,000,000,000 reward). The second kingdom is for those who love others (the $1,000,000,000 reward). The third kingdom is for those who who love themselves ($1,000,000 reward). A loving God wants to bless ALL his children and we each choose how much we will receive at his hands. No one is assigned to a kingdom until they have completed their "hell". You pay everyone back, make everything right, grow as you needed to and go on to your reward. Even the worst of us will be blessed for having this earth life.

The Doctrine and Covenants 19:4-19 explains that since God is endless, punishment at his hands is endless punishment but it does not last forever, just until we pay the price for our sins (sin being anything that keeps us from becoming our best self).

So, Mercy claims those who ask for it through turning to Jesus Christ and giving yourself to him and Justice is what everyone else gets. God who loves us will bless us each with as much as we are willing to accept. God remains both a merciful and just god committed to our growth and development.

"This is my work and my glory to bring to pass the immortality and eternal life of man." Moses 1:39

Assuming hypothetically for the sake of logical analysis that the doctrinal Hell you have described does exist: since that particular Hell is a natural feature of the Universe and not a real person or entity (it is rather a place or a spiritual condition) it cannot be evil -- because evil originates in the mind.

Psychology Today, Why Is There Evil? (2017, by Paul Thagard, PhD)

BBC Future, Psychology: the Man Who Studies Everyday Evil (2015, by David Robson)

Start finding the word "Hell" in the Bible. Some translations may have it as an interpretation, but if you follow the sources strictly enough you won't find it.
You'll find "Sheol" as a resting place. You'll find "Gehenna" as a valley that in old times were an offering place for gods like Molog and Baal and ended up as a garbage pile. And you'll occasionally find Tartarus as a place for the fallen angels. But not Hell.

It's widely argued the concept of "Heaven" and "Hell" wasn't invented until early Christian and Roman faith intermixed, as a "Christian" take of the roman "Hades". All you can find in earlier literature is reference to places like "Sheol" and Jesus, in one single discussion, making a parable about a servant ending up in "Abrahams bosom" when his rather frugal master did not. When Jesus made a lot of parables and it's doubtful how literally they can be taken.

What you can find is Paul and other early disciples fighting for the idea of being woken up to a new life. Not an ethereal one but material, with new bodies. That death from this life is not final, and that the ones God choose to trust will be given new bodies that won't die.

You'll find this being extensively discussed in the Book of Revelation, but the topic is mentioned here and there during the whole Bible. It's an evolving story, all the way from the fall of Adam and Eve.

There's been a renewed focus on this in later years, because sure enough, the idea of heaven and hell is not ethically defensible. If you want to defend Christian faith you'll have to find something better and stronger. and that's when you begin to read your Bible with new eyes.

When it comes to God's wrath, I like how N.T. Wright described it: "God hates sin in the same way a violin maker would hate to see one of his beautiful creations used as a tennis racquet." Sin is to behave in a way that would long term harm your and/or others, it's originally an archer's term that means to "miss the mark". Do you behave in a way that really works towards the goals you want in your life, or do you not?
The sad thing is, this has all been used to control other people instead of helping them grow, which according to the Bible will meet final judgement one day and surely will be regarded as sin. Paul. for one, warned against behavior that would make people revolt, and this is exactly that kind of behavior.

In the beginning, God created the heavens and the earth. Gen 1:1. Nowhere in the Bible is it stated that God created Hell. God has always allowed man choice. To listen and obey his requirements, or not. Man was given eternal life, and death was mentioned ONLY if disobedience occurred to Gods command. Man was told that if he disobeyed, he would die and his flesh would be returned to the dust from which it came. Death was the penalty of disobedience, not life in eternal punishment, as most "fake religions" teach. The Bible speaks of resurrection, a returning back to life. Gods original plan for man did not include death, but everlasting life. "All those in the memorial tombs will hear his voice and come out" is the promise for our lost loved ones. A resurrection of the righteous and the unrighteous. The concept of a burning hell is a LIE!

In many religions, for example, the Abrahamic ones, there exists a
place of eternal punishment for those who live in violation of God's
commandments. Assuming an infinitely-long afterlife, in which
"sinners" are punished with all the punishments deemed appropriate
that Hell has to offer... doesn't that make God commit more evil than
good by allowing those sinners to experience Hell?

It depends on how you define and measure evil and good. In particular, the answer is a clear "no" in any belief system that views its God as the standard of goodness, or in any in which good and evil are only recognized as characterizing human actions.

Surely, whatever
evils committed while the person in question is alive are finite,

Are they? The duration of any evil acts a person commits in their lifetime is certainly finite, but even from a human perspective, duration is a poor measure of evil. What about the consequences that follow from evil actions? Should not the nature, scope, and duration of those be considered? And if we posit a created universe then we can imagine that there might be consequences even outside the universe, and who can say whether our concept of finiteness even has any meaningfulness there?

while, as (to my understanding) the punishments suffered in Hell are
infinite.

Are they? Suppose Hell is outside the created universe that we have posited, which makes a lot more sense to me than it being inside the universe as I normally mean that term. How do you measure the punishment? Can you even be confident that we have any concepts that would be applicable to measuring?

Note, that this question assumes that God is able to stop the
existence of Hell and the infinite punishment of evil committed by any
man. Thus, making him evil by exerting infinite amounts of suffering
to the sinners by inaction.

Well of course you can reach your desired conclusion by assumption, or by making enough assumptions and definitions of your own choosing to support it. The result of such an effort is contingent on the validity of the assumptions and shaped by the definitions of the terms in which the argument is expressed. It is a useless exercise if those you are trying to persuade disagree with you about your premises.

The closest to this in the bible (I can't comment on any other source from Islam for example) is the lake of fire, which the devil, the beast and his accomplices will be cast into after the 1000 year period where he is let loose upon the world. It is used four times in revelations, two of those times it talks about the devil, the beast and his accomplices, together with the false prophet they will be thrown into the lake, and only one of those times speak about being there forever. The other two times it adds those that are not in the book of life, and it is also added in these two cases that it is referred to as the second death.

It's possible that the eternal suffering and the second death refers to the same thing or two different events. And it's not sure which is meant literally. Because it says suffering forever and ever one place, and second death (which sounds like ceasing to exist).

On the question of whether the existence of the lake of fire makes Him evil, fundamentally goes against the idea of the lake in the first place. It is a just punishment for sins, and God's mercy and grace, sending Christ to die for the world is what makes it possible for us to forgo that just punishment. Rejecting that love is not on Him. And the existence of just punishment does not make him evil.

I raise until you the trilemma of Hell.

Define: God is good

Assume: a man who will be evil if given the choice

Choose:

• Mankind has no choice but to not be evil. Ergo: love does not exist.


• Evil men go to hell forever.


• Evil men are destroyed utterly.

C.S. Lewis wrote that Hell is locked from the inside. This but pushes the trilemma back one level of abstraction and does not change it.

Propound to me a choice where you would call God good. Even if you manage to find a case that I have not heard, I doubt you can change the outcome.