the idea is that you literally cannot test the existence of a god.
Not directly, no. But most religions make numerous testable
claims, such as the age of earth
And when claim after claim after claim is proven false, you're usually left with two explanations, either "god is deliberately deceiving us" or "perhaps it's not a coincidence that this god's knowledge is the same as the knowledge of the people at the time that belief in him originated." Which you choose depends on what kind of pursuits you follow; emotional or intellectual (Note that I'm not saying believers are dumb)
It's only these gods I claim to have
any degree of knowledge over. And even then I'm not claiming absolute knowledge, just "I'm pretty sure"
There's uncountable religions I don't know anything about, and thus I can't claim
any degree of knowledge over their gods.
And the deistic approach of "there's a god and he exists and that's it" will never be testable and thus no one can claim knowledge over that.