This is a fundamental misunderstanding of Russell’s Teapot. If someone claims there is a teapot floating in space, cool, they need to prove its existence and the rest of us can go around as if one doesn’t exist. If someone claims there isn’t a teapot floating in space, now the burden of proof is on them. We can quickly exercise some critical thinking and realize that, while there might be a teapot in space someone brought with them and left, it’s not going to be beyond the asteroid belt.
Now do every belief system with empirical evidence. You can’t, primarily because belief in the logic used to prove that empirical evidence is the best evidence is itself a belief system. Changing any one of the axioms that underpin your methodology completely changes the methodology (eg parallel lines meet at infinity turns geometry into hyperbolic geometry). Furthermore, we can extend Gödel’s incompleteness theorems to any formal system, like you’re attempting to employ, and show that they can’t prove themselves.
In other words, we must take things on faith if we want to use logic and pull out statement related to logic like “burden of proof is on the positive.” You can believe whatever the fuck you want; you just can’t prove it and, in most metaphysical cases, you can’t disprove it either.