Take almost any debate about God’s existence between an atheist and a theist and you can pretty much summarize it in a simple exchange: “Can you prove that God exists?” “No, but can you prove that he doesn’t?” And of course the atheist cannot. Unless she’s Ayn Rand in which case she’ll just state that “you are never called upon to prove a negative.” But that’s cheating. Clearly we are in this case, you can’t just define the problem away with your own axioms. And in a strict sense there’s no way to disprove the existence of God scientifically, since scientific methods cannot disprove (or even prove) anything with a 100% certainty.
But that’s not the whole truth. We can, in fact, start by examining any evidence that does support the existence of God. This is all well within the domain of applicability of science. Visions of afterlife? Nah, your brain is probably just lacking oxygen. A burning bush? Well, there’s this plant in the Levant region that emits these flammable oils. And so on. And if by some miraculous feat we could disprove all the possible scientific evidence for the existence of God, we could say: “Sure, God might exist, but since he has never interacted with the physical world (mind you that the existence of even supernatural events could be established scientifically), your concept of him is based purely on guesswork and thus, even if he does exist, statistically speaking, he’s almost surely not like you imagine him to be.” So in the end it comes down to scientifically examining the evidence available, for and against.