The Question: Doesn’t the fact of suffering prove that God doesn’t exist?

In some respects, this question is related to the question of God’s omnipotence.  If God existed and was omnipotent – that is, able to do anything God wanted to do – then surely God would do something about suffering, given that it was within God’s power to do so.  The fact that God doesn’t do anything about suffering therefore surely proves that God doesn’t actually exist.