Atheists aren't saying "there is absolutely no possibility of a god!" In fact, we understand that the possibilities are infinite.
However, admitting that a possibility exists is not a concession that the possibility has any merit of likeliness. We also admit there's a possibility that there's a Tyrannosaurus Rex standing outside, ready to eat us. The next step is gathering any evidence to support the claim.
Ultimately, when one asserts anything, the burden of proof is on that person to demonstrate that the assertion is accurate beyond a reasonable doubt. No one is required to accept that claim until this burden of proof is met.