By the God hypothesis, I take it you mean the belief that an all-powerful, all-knowing, good God exists. If this is the hypothesis, it is falsifiable. If such a God exists, there can be no unnecessary suffering. If unnecessary suffering exists, God does not. We can be sure of this because God would be able to eliminate unnecessary suffering, would desire to eliminate unnecessary suffering (since he is good), and would know how to do so.
That is the falsifiable prediction a God hypothesis would make. Every instance of suffering would have to have a purpose. You can see the need for purpose any time a preacher says "God works in mysterious ways." The baby who burned to death in a fire did so in order to go to heaven and also bring us all closer together. The real problem would be then to determine if any suffering is in fact unnecessary.
For suffering to be necessary, it would either have to benefit others or benefit oneself. For humans it is possible that, given the garden of eden mistake, all suffering is deserved. But once we look to animals, we see that a lot of unnecessary suffering goes on. We know it is unnecessary suffering because the animals lack free will. They cannot be punished, any lesson they may learn could be implanted in them with no need for actual pain, and any lesson taught to others could be taught with the mere appearance of pain. As long as we are going to trust scientific evidence that animals really feel pain, we have solid evidence that God does not exist. The God hypothesis would postulate a world where all suffering has purpose. But the suffering of beings without free will can serve no purpose (because whatever end would be achieved by that suffering can be achieved otherwise), and hence falsifies the God hypothesis.
Interestingly the God hypothesis is only made falsifiable by the absolute claims it makes (all-powerful, all-knowing, etc.) A less absolute God hypothesis (Zeus, for example) would likely not be falsifiable.
