My question is why people are so obsessed with this question, like it matters?
We can all alleviate someone's suffering or at least try. It's better use of one's time than debating whether there is a loving deity or not that can or won't or can't alleviate suffering.
The whole idea that one's convictions are the important thing is rubbish. Who cares if you believe in a god or you don't believe in a god? What good does either conviction do if you spend time arguing about how superior or more correct your views are, time that could have been better spent elsewhere?
One side says: Oh, it's important to debate because we have to convince others to save souls from hell.
The other side says: Oh, it's important to debate because we have to convince others how destructive such a false conviction is.
The only convictions that need to be changed are the ones that tell you that beliefs are more important than actions and that we need to alter other people's minds instead of doing something to make the world a better place.
The biggest lie is not god mythology, it's that it is impossible for us to put an end to suffering or that it takes a god to do it--that's the really big lie!
Suffering exists and doesn't get alleviated because people have the ability to do something to stop it and don't. They would rather argue over issues to ignore the fact that they aren't doing anything. Suffering neither proves or disproves divinities. Suffering only tells us how little we humans really do for one another. And it ain't much.
Suffering is definitely proof that there is no G-d, but not that G-d doesn't exist somewhere out there. Suffering is proof that G-d doesn't exist in the most important of places. Suffering is proof that G-d doesn't exist in you and me. And he doesn't exist in us not because we don't believe in G-d but because we don't care to believe in one another enough to find ways to alleviate each other's suffering.