It doesn't cut both ways because any common definition of God is inherently not testable, and thus excluded for science and notions such as evidence. It is a matter of faith which is largely a separate area of thought.

In short, regardless of what any individual believes, to science itself, God does not exist (unless He ever made Himself testable in some form).

> to science itself, God does not exist

If you suppose the absence of supernatural factors, of course you cannot conclusively prove the supernatural. Any why does science assume there are not supernatural factors? Well, there are valid reasons, but to a theist that's merely a model of reality for the purpose of discovery and pedagogy.

But to take the premise as the conclusion is a logical fallacy. And on top of that, the underlying premise (assume only the physical and measurable exist) is a metaphysical premise and outside the purview of science.

It is a direct consequence of only concerning itself with what can be tested. If it didn't, then it would no longer be science.