Surely a perennial question to be sure. Why would a just and moral God allow so much suffering in the world? I've certainly been grappling with the question for years. Atheists feel free to chime in. But remember that the question is (hypothetically, if you will) why would He allow so much suffering. If you simply say there is no God, you're not answering the question . BTW if anyone is wondering, the name for the vindication of God in the face of evil is theodicy. So if you ever want to study the matter on your own, use that as your key word. (I'm sure Google alone has many hits for that word.)
He doesn't allow suffering per se. Man was given the will to choice, and what you rather have: sterility, or fertility? It's like pruning a plant so that it doesn't wither, and in life we must experience suffering so that we don't wither. Suffering & Happiness are two sides of the same coin. Something that I live by is, "every fear unmet is a step further from freedom," so that by suffering we grow. Have you read Nietzsche's Birth of Tragedy?
An anthology of Bronze Age mythology prefaced by a story of a talking snake with a magic apple in an enchanted garden postulates that God is an arsonist fireman; setting fire to your house in the middle of the night with you and your family inside so that he can rush in and play the hero by saving people who he intentionally put in jeopardy in the first place, then demanding constant and unfailing adulation under threat of eternal torture. Throughout the Old Testament God is portrayed as a petulant, brutal, capricious, and murderous tyrant; a god allegedly of love which perpetually threatens and torments humanity with suffering, death, and eternal damnation unless they continually stroke his ego like some battered spouse who's been tortured into some 'Stockholm Syndrome' delusion wherein they see their abuser as all just and all powerful and their suffering as their own fault for not being compliant and servile enough...a god who in the New Testament mercilessly tortures his own son to death to fulfill some perverse legalism of his own contriving to prove how "just and moral" he is. The whole premise is simply too preposterous to wrap one's mind around.
I'm no theologian, but there is a possible solution to your conundrum. You mentioned that God is just and moral, but is (S)he omnipotent? The theodicy problem results from the perceived conflict between the existence of evil and injustice, on the one hand, and God's supposed omnipotence on the other. This assumes that God is a hands-on anthropomorphic micromanager. But some of us believers conceive of God in more deistic terms as the Ground of Being, Brahman, Ultimate Meaning, Higher Power, etc. Theologian Charles Hartshorne and other Christians who are into "process theology" say God might not be omnipotent (Hartshorne, Omnipotence and Other Theological Mistakes). Hartshorne was heavily influenced by the process philosophy of mathematician Alfred North Whitehead, who viewed the universe as a dynamic web of interrelated processes, of which we are integral parts. Process theology includes God in this network of changing, co-evolving systems. God, and our knowledge of God, is constantly developing. God's omnipotence/omnisicience can't mean that (S)he can know and control everything, since omnipotence includes the ability to confer free will, and if a being truly has autonomy its behavior can't be predicted even by a so-called omniscient being. Nor, by definition, can it be completely controlled. Interestingly, omnipotence isn't mentioned in the Bible, although "Almighty" appears in virtually every book of the Old Testament, often dozens of times. Sometimes readers use those terms interchangeably, but theologian Diogenes Allen (Theology for A Troubled Believer) argues that they aren't the same. God cannot do things that are logically contradictory, so (S)he is not omnipotent. Thus, if God chooses to give us free will, that limits control of us. And if God chooses to do the same for the rest of the universe, as the late Catholic paleontologist and theologian (not in favor by the Vatican) Fr. Teilhard de Chardin proposed, there goes the theodicy problem. I think that many of the world's problems are attributable to the exercise of free will by humans, and the others result from the operation of the natural laws of the universe which have a way of taking a toll on us humans. I attend Catholic bible study which always opens with prayer requests--to heal people we know who are sick or infirm, or have success in some venture, or who are having various troubles in life, and to bless our country and guide our leaders. And I often wonder--do these people seriously believe that the God of the universe will change the laws of nature to accommodate these requests, or (worse) will let some kid or loved one die or stay sick if they aren't included on the prayer list? And yes, I think most of them may believe this. I think, in a way, that shows commendable concern for our fellow human beings. But I, for one, expect the laws of physics and biology to operate as they always have, even at the expense of poor Aunt Millie or some other unfortunate person. And in the long run, I think that's not such a bad thing, and we're better off accepting that reality unless there seems to be something we can do about it . As my brother liked to say, as he was slowly dying of cancer: "It is what it is."