As an initiation rite, Brazil's Satere-Mawe people make gloves with hundreds of bullet ants woven in, stinger pointing inward, and the boy who wants to become a man is expected to wear them for ten minutes, and the incredible pain lasts for hours. According to the Schmidt Sting Pain Index, the bullet ant sting is the worst of the Hymenopteran stings. Schmidt describes the experience of a single sting as follows: "Pure, intense, brilliant pain. Like fire-walking over flaming charcoal with a 3-inch rusty nail in your heel." (Here is a man dedicated to science.)
Now, consider this. The boy suffers horribly for a large part of a day, but then he's a man for half a century. The memory of having stood up to close to the worst pain that nature fling at him has a deep value. How much value? It need not be so great, actually, for the ordeal to be worth it. Let us suppose that the disvalue of the suffering is 10,000 units. Then as long as he gets a mere four units of value from the suffering for every week of his life (say, he remembers the experience four times a week, and it gives him one unit of value each time), it is worth it. The longer his future life as a man, the greater the value. (This is just for priming intuitions. In fact, we need to contend with incommensurability.)
Now, maybe, in this case the pain is just much too great to pay off sufficiently in added meaningfulness over a future 50 years. Having skimmed (too painful to read carefully!) the description of the pain, I myself doubt it is worth it. Though it has to be noted that unless the adult men of that community are by and large sadists, in their judgment it is worth it, and they're better judges than wimpy I! Still, let us grant that it's not worth it.
But still, maybe a minute of wearing the ant-gloves would be worth it, if it made more meaningful a future manhood of fifty years. Scaling, ten minutes might be worth it if it made more meaningful a future manhood of five hundred years.
The point here is that a painful initiation ritual will be worthwhile if it makes more meaningful a future state of sufficient length. But now suppose that I am going to live for a million years. Then it does not seem absurd to say that a year of quite severe suffering could be worthwhile as an initiation ritual. Suppose I am going to live for a billion years. Then a hundred years of suffering might well be worthwhile, given the added value over the course of the subsequent 999,999,900 years.
But in fact if theism is true, then very likely we will live forever, since it is very likely that a good God would want persons to live forever. If so, then a suffering-filled initiation ritual that lasts for about a century would surely be justified, even if it only added a little value to each subsequent day (as long as the value did not quickly tend to zero in the limit as time goes to infinity).
Let's put it this way. It seems not improbable that if God made a person that was going to blissfully exist for a year, God could have justification to allow that person to suffer intensely for a second first. If he made a person that was going to blissfully exist for a ten years, he might easily find justification to allow that person to suffer for ten seconds first. And, by the same reckoning, if the person were to exist for three billion years, he might find justification to allow her to suffer intensely for about 90 years. After all, 90 years is to 3 billion years as a second is to a year.
Or consider it this way. Suppose you're going to live for three billion years, but every year you will experience a second of intense suffering, in a way that contributes to the meaningfulness of the rest of your life. It does not seem absurd to suppose that God could have a reason to arrange things so. But if so, then it likewise should not seem absurd to suppose that God could arrange it so you'd suffer 90 years, and then live out 2,999,999,910 years of bliss. And if we live not just for three billion years, but forever, this is even easier to imagine.
In the face of eternity, a finite amount of suffering is just a blip.
But does it not beg the question to suppose eternal life in responding to the problem of evil? Not at all. The problem of evil is an argument against theism. Theism makes eternal life for any created persons very likely. Thus, if the problem of evil is to make a significant dent in the probability of theism, the problem of evil has to work even if there is eternal life, or else a good argument against eternal life is needed.