If I (an atheist) may go against both theists and atheists here, all this talk of evidence and falsification is a little further down the road than the OP’s question, which I think is more to do with Ockham’s Razor, and which version of it (if any) one ascribes to. The version to which I, and I believe most reasonable people, ascribe (if only in an unspoken manner) is this:
If a natural explanation exists, no supernatural explanation is necessary.
This is very close to Newton’s version, and remember how theistic he was. It is also a principle we use in everyday life, wherein we simply don’t jump for supernatural explanations for the world around us when natural explanations which have passed the most rigorous tests, devised by the finest minds, for centuries, are there for all to see.
Now, the claim “There is no god”, viewed in the light of OR, is really the claim “There are no longer any explanatory Gaps big enough for god to fit into”. And it is (and I might find quite some disagreement here) only an opinion. I cannot prove that even so natural a phenomenon as lightning is not simply Zeus’ anger. I can only demonstrate how the phenomenon correlates every time with some natural mechanism we understand pretty well. Anyone is free to either posit a Cosmic Joker of a god who lays false electrical trails, or point to those elements of lightning we don’t understand (and if there were no such elements, we could close science departments worldwide since there would be no more science to do!) and say “Those Gaps are where god fits”.
So, I believe that cosmology, abiogenesis and cognitive science today close all of the explanatory gaps so small that positing god there is like involving him in making lightning. But I will never “prove” this, since “proofs” require everyone to agree on initial premises, and what is “agreement” but a coincidence of opinion?
Having said all that, I simply don’t understand why gods are the historical default! I have just as many questions about how they come to exist, rather than not, as I do the universe. Ockham’s Razor thus shaves away such further steps in my mind, leaving me with questions about what I can see and test (perhaps indirectly) than what I can’t. And even god “showing itself” would not affect my considerations, since my senses could be being deceived by an alien holodeck or future simulation. Effectively, my atheism is itself unfalsifiable, because there’s nothing I can imagine to which I would attribute a supernatural explanation before a natural one.