So I ask here, can anyone prove to me that atheism exists?
It’s not our job to.
The way this works is that the burden of proof falls onto the person who makes the claim. Any claim. In this case the claim is “I am an atheist”, which simply means, “I do not believe in a god”.
So the next question is, what amount of evidence would satisfy that claim?
To figure this out we apply a very basic principle of reason: extraordinary claims require extraordinary evidence. In other words, the more out of the ordinary a claim is the more evidence one would need to justify it.
”I do not believe in a god” is by no means an extraordinary claim, in fact a statement by an individual regarding what they believe is one of the most mundane claims anyone could possibly make.
In addition, there is also a “default position” principle involved here; you either accept the claim until proven otherwise, or reject the claim until proven. In this case, rejecting someone’s stated beliefs until proven puts you in a situation where essentially nothing can be believed and you accept nothing about what anyone believes. That leads to absurdity.
Therefore, absent any evidence to the contrary, the only rationally defensible position is to accept the claim until you have a reason not to.
Burden satisfied. You’re welcome.