If any non-falsifiable evidence of a god's existing came to light, I would be persuaded to change my mind.

Is what many atheists claim and the basis for the Agnostic Atheist position. But have have they ever thought about what criteria said non-falsifiable evidence would have to take for them to accept it?
(EDIT: the evidence need not only be non-falsifiable; this post was based off a quote from a member and I should have been more careful with paraphrasing them)

See if you've not thought about this prior, then you will never accept any evidence since you've no standard by which to judge good vs. bad evidence.

Consider I turn water into wine in front of you.
Is that enough?
After all, you could claim that it's merely a chemical reaction and not divinity.

Consider I walk on water in front of you.
Is that enough?
After all, you could claim that it's merely a new form of propulsion or special shoes that allow me to do that.

Consider I die and come back from the dead.
Is that enough?
After all, you could claim that it's merely a great advance in medical technology.

So my point, and question, is if you are atheist and carry the a priori viewpoint, be it belief or knowledge, that gods dont' exist, how do you combat the bias inherent in that viewpoint in order to objectively, dispassionately, and fairly evaluate any evidence that claims to speak about gods?

And as a follow up, as an atheist how do you combat scientism? The belief that science can and will explain everything makes any evidence of godhood just science not yet understood and thus there can never be any evidence to change your mind away from atheism.