I've never know anyone to give an emotionally satisfying answer to the question of why God allows or uses suffering. But, this assumes that assuaging our feelings is the goal of such an answer. It's as if we expect an answer during suffering that results in, "The pain is terrible but I feel good about it now." That's just silly.
There's a difference between the experience and emotion of suffering and what we know, intellectually, about suffering and God's role in it. So, allow me to make a few sweeping observations about what we know, not what we feel. God is not responsible for our suffering. Though God is not responsible he chose to act regarding the greatest cause of suffering—sin. Jesus' suffering and death is The beginning of God's answer to suffering.
God is not obligated by our suffering. Though God is not obligated he chose to act by experiencing suffering with us. Jesus chose, of his own free will, to suffer horrible abuse and an agonizing murder. Therefore, he can identify with our suffering.
God is not on our timeline. God sees the larger picture, the long view. We don't. Suffering will one day be eliminated for those who know God. But not now. We have to wait. And if we don't like it, well, tough.
While some are busy questioning God's justice or role in suffering, I think it's valuable to look at our role.
Man is responsible for suffering. Sin produced suffering. Man sins. Thus, man causes suffering. We are the responsible party, not God.
Man is obligated by his suffering. Because we facilitate suffering we are responsible for relieving it. Blaming God never relieved anyone's suffering.
Man must act quickly to do something about suffering. If we do not act, suffering increases and we become partly responsible for not acting when it is our responsibility to act.
Here is a truth we cannot avoid: We cannot truly know God without suffering.
Without Jesus' suffering we cannot know God. Suffering is part of God's plan to know him. Jesus had to be willing to suffer so that we can know God more fully.
Without our suffering we are limited in knowing and experiencing God's character. We cannot experience God's wonderful attributes of forgiveness, grace, mercy, and favor apart from suffering. Thus, to not experience these things is to limit our knowledge of, and experience of God.
Without other's suffering we cannot express God's character that others might know him. Suffering is our opportunity to express the love of God within us. Without suffering we cannot fully represent God on earth.
While these things are intellectually true, they may not help our emotional pain when we see extreme suffering. But, God is not obligated by our emotions. This may make you angry. But, God is not obligated by your outrage. There is no moral imperative in existence that makes God responsible for eliminating our suffering. If you think there is, then where does that imperative originate? If with us, then who has authority to say God must do what we command? We have a word for this: slavery.
Though it may seem counterintuitive to what I've written here, there are things which do obligate God. God is obligated by his own love, justice, and knowledge. He alone chooses how he will act, when he will act, and for what reasons he will act. If we think we can impose these upon God, then I ask, who has ever successfully imposed anything on God? God's solutions to our problems are taken according to his knowledge, not ours.
If you live to be 100 and spend most of those years in suffering, but then spend trillions times trillions times trillions of never ending eons in heaven with no suffering, then what will you think of those brief 100 years? Chances are you won't regard them as significant or worth thinking of ever again. But this is true only if you know Christ. If you do not know Christ then you will go to hell. In hell, you will regard all the good things in life you had to be meaningless compared to the trillions times trillions times trillions of never ending eons of suffering you will experience.
Bottom line, if you're upset about suffering, then do something about it. Give. Volunteer. Minister to the needs of others. But, stop blaming God for what you are responsible for, or responsible to do. Denying God's existence, or his justice, and blaming God never relieved anyone's suffering. In fact, denying God and blaming God will only contribute to your own suffering. And what good is that?