It's often claimed that theism is untestable, but that seems to me mistaken. Surely we should expect significant differences between an atheistic universe and one guided by a supreme being that is all-powerful, knowing, and benevolent. Indeed, this is precisely why the problem of evil is such a powerful anti-theistic argument: it rests on the idea that the world is not how we would expect it to be in light of such a being's existence. We would expect God to create the best possible world, which ours does not seem to be. That's one failed prediction for theism, and thus a count against the theory.
The argument from divine silence rests on a similar inference. If the Christian God existed, he would surely let us know this. Perhaps each Sunday he would light up the skies and speak to us in a booming voice, or something along those lines. But of course nothing like this actually occurs. At present, the epistemic situation of many individuals provides them with little or no reason to believe in God. This is not something we should expect to be the case if God really existed. (Indeed, I think it makes traditional Christianity completely ludicrous - see my argument from hell.) Thus we have a second failed prediction for Christianity, and another serious count against the God hypothesis.
Now, it must be granted that these failures do not conclusively falsify theism. But then, I'm not sure that empirical evidence can ever conclusively falsify anything. Suppose I posit the existence of a black hole near our solar system. Others might cast doubt on this by showing how the standard predictions we'd make from this hypothesis fail to match up with our observations of reality. But I could always respond by claiming a measurement failure on their part, effectively denying their observations; or I might suggest that they have misunderstood the nature of black holes, thereby disputing the legitimacy of their predictions; or I might simply say that extraordinary circumstances allow for the possibility of the black hole's existence no matter how unlikely it may seem given our evidence. (Evidence can be misleading; improbable events may still occur.) The same responses are open to the theist. But of course they are unconvincing in either case.
These problems might be avoided by reverting to an extremely weak notion of 'God' as a causally inert being that makes no difference to the universe. As in the case of my positing a causally inert blob that likewise 'is nowhere' and 'does nothing', we surely have no reason to believe in such a pointless entity. Ockham's razor can safely shear it away.
But I'm sure most theists do not conceive of their God in such a useless way. So Ockham's Razor, or complaints about 'unfalsifiability', should not be the atheist's first line of attack. I think much stronger arguments can be made by taking the God hypothesis seriously, i.e. as making testable predictions about the world, and then pointing out how dismally those predictions line up with reality.