When considering this question, it’s not advisable to do so with an emotional appeal. In order to address this question effectively, we must do so from an intellectual perspective . . . not an emotional one.
To ask, “What kind of God would allow evil and suffering in the world?”, is an emotionally loaded question, indeed. This only makes the question more difficult to deal with, even if the answer is actually relatively simple.
I think we first need to ask, “Is it even possible that God would allow evil? Is it possible that God might have sufficient reasons for allowing evil?” If it is the case that either of these are possible, there is no inherent contradiction between the existence of God and evil.
Perhaps it’s possible, but it may not be probable, that God would allow evil. Although I can appreciate this retort, I don’t think we are in a place to conclude this with any real certainty. After all, we are only finite beings with limited knowledge.
Speaking of knowledge, God, on the other hand, is an infinite being! He has infinite knowledge, along with His other attributes to being, such as power and morality. If God is an infinite being, His other attributes would also be infinite, or maximally great. We might rightly say that God is the greatest conceivable being, in that He is all-knowing, all-powerful, and morally perfect. This is precisely why God is worthy of worship. If God was flawed in any way, not only would He not be worthy of worship, He wouldn’t be God. As a matter of fact, this is exactly what the Christian means when they say God: He is maximally great and worthy of worship.
Could it be that God allows pain and suffering in the world because He has morally sufficient reasons to? I certainly think so. If He didn’t, He would be morally flawed and would not fit the definition of God; He would not fit the definition of being the greatest conceivable being. If this were the case, it would be inconsistent with what Christians believe and what Scripture affirms. To say that Christians believe in a morally flawed God is actually self-contradictory and, thus, self-evidentially false.
So . . . if it is possible that God would have morally sufficient reasons for allowing evil, what might those be? Could it be that since we were created with free-will, evil is an inevitable byproduct? Could it be that God uses pain and suffering as means to draw people closer to Himself on some occasions? I know all kinds of people who have come to a knowledge of God for precisely this reason, so I think that could certainly be the case. Or . . . think of natural disasters, such as the hurricanes last year that followed that of Harvey; there were hundreds of people getting saved during that time, despite their tragic circumstances. Is it possible that in order to have genuine love, you would have to create free creatures that would have the freedom not to love? This would allow for all sorts of vulnerabilities, just like it does for your husband, wife, any significant other.
I think we need to be careful asking, “What kind of God would allow pain and suffering, or evil in the world?”, especially when it comes to the Christian God, considering the pain and suffering He experienced on the cross; that type of pain and suffering will most likely never be experienced by most people in life.
Moreover, what is pain and suffering if God does not exist? What objective basis does the naturalist have for saying that something is good, bad, or evil? Is it because they say so? How is that any different from what anyone else says, whether it be Hitler, Stalin, or whomever? If there is no objective basis, morality is meaningless. If there is no objective good, there is no bad. The world just simply is. It’s almost as if saying something is bad or evil immediately posits an objective standard of good, but what is that standard on atheism? At least the Christian can say that that standard of good is God, but what can the non-theist say? It’s almost as if the existence of evil, paradoxically, proves the existence of God.