Is There a God That Allows Suffering?

A lot of people say that God has some other purpose, which he seeks to fulfill such as free will. And the idea is that there's some kind of metaphysical or logical impossibility with God bringing about a world of free creatures and there being no suffering. So in a sense, something like a free will defense says, well, there's just no way to bring about free will without suffering. But I don't know if God is like obliged to make it better.