Q about arguments for God's existence.

[Dystopia]

I have a question about atheists and the burden of proof:
If the theist claims - "God exists" - Obviously it's evidence or GTFO
But what if the atheist claims - "God is bullshit", or "God doesn't exist", or even "God probably doesn't exist" - Doesn't this shift the burden of proof? After all and if I'm not mistaken the scientific method states that if you make a negative claim (that something doesn't exist) you still need to provide proof

So my question is - Don't atheists have the burden of evidence as well when we make claims? For example - If we say "atheism is rational and theism is not" I think we should be required to provide evidence to explain why atheism is better than theism (Not that it is hard or anything)

Atheists mostly don't need to provide proof, and we are well aware of that, specially when theists claim their religion is right or that god exists; but often we will make claims like "Your religion is false" or "Your god is evil" and it is my opinion that there's no reason to not shift the burden of proof here.