In Who has the Burden of Proof? Atheism vs. Theism, Austin Cline (ThoughtCo) provides an outstanding discussion of something every atheist (and every religious believer) should understand. Atheism (i.e., a lack of belief in gods) is the default position, the place from which everyone begins. This means that the burden of proof always lies with the religious believer who is claiming that some sort of god or gods exist.
It is not necessary for the atheist to claim certainty that no gods could possibly exist. Atheism requires no such certainty. Typically, the atheist's position is simply that the religious believer has failed to meet the burden of proof. If that were to change (i.e., a religious believer comes forward with sufficient evidence to support god-belief), rational atheists would abandon atheism.
The religious believer is making a specific claim that a god or gods exist. Such a claim requires supporting evidence if it is to be accepted rationally. Without such evidence, it is not rational to accept it as true. This is why appeals to faith are offered in the religious context; however, it is important to note that such appeals are not accepted in any other context. If I tell you that I communicate with my dog telepathically, you'll ask for evidence. If I provide none but merely insist that you have to have faith that what I'm claiming is true, you'll rightly laugh at me. I see no reason why this shouldn't be the case when it comes to claims about gods.
It is not up to the atheist to prove that no gods exist. It is not up to the atheist to somehow provide proof of atheism. It is up to the person making the claim that gods exist to provide evidence sufficient to support his or her claim. As long as he or she fails to do so, atheism is the only rational position.
An early version of this post appeared at Atheist Revolution in 2005. It was updated and expanded in 2018.