Hi,
No I'm sorry but this isn't something that "works both ways." Let's remove the specifics of this particular argument/belief for a moment (theism/atheism) and focus on the proof principle in general.
If a person posits the existence of something (anything at all) then the ONUS is on this person to provide proof of its existence, if indeed the person feels that it is possible. The onus is NOT on anybody else to demonstrate that the thing does not exist. Any other approach is irrational and would mean the entire world's population could live in a fantasy world divorced from reality. I could, for example, claim that there are giant pink hamsters living on the moon. It is up to me to provide evidence of their existence. Every one else may say they do not exist but the onus is not on them to provide evidence that they do not exist since it is me that is making the claim for their existence and so it is up to me to provide the objectively assessable evidence. This is simple sound logic which applies to any proposition, whether it is for my lunar hamsters, gravity, evolution, deities, nirvana, salmon, Santa Claus, blue cheese, black swans or hell.
s.