The Evidence Required Is?

[Welsh cake]

Sincere question, is this opinion held by pretty much every atheist here or do some believe that the physical universe is governed by consistent laws? It seems to go contrary to the basic assumption of scientific inquiry.

You need to exercise a little scientific discipline here, the universe isn't governed by our scientific laws. The laws themselves are simply analytic statements, observations about reality that usually feature an empirically determined constant without exception. Laws explain the fundamental interactions of our universe but they can't explain why those interactions are constantly occurring.

It [math] did not exist independent of minds before the big bang, that's absurd.

Anyone can imagine an alternate universe with different physical constants. No one can imagine a physical universe where logic and math do not work, that would be absurd, literally.

Irrelevant. I'm not talking about the human imagination! I'm addressing your comments on the philosophy of mathematics, specifically your claims on mathematical realism. Kindly stay on topic.