Okay, so this may not really be a scientific question, but rather a philosophical or linguistic one, but hopefully someone could help me out here.

So let's assume there's someone who claims that they BELIEVE in science and anything that cannot be proven scientifically DOES NOT EXIST.

Obviously this person tries to argue against accepting things that have never been proven to exist, as real (so gods, etc.). But they way it's formed has a built in flaw, where it says that anything that hasn't been proven (YET) simply does not exist at all. So if, for example, it was used few decades ago, someone would claim that atoms or quarks don't exist, period.

So as I see it, it's a logical fallacy, because it rejects anything that wasn't scientifically discovered and documented yet. My question is, how would that fallacy be called? Or does it even qualify as one, or maybe it's a combination of few?

I tried to read a bit about different philosophical views that could match it more or less, and found out that positivism (which came from empiricism) is probably the closest one IN THEORY. And as far as logical fallacies go, the closest two I found are argumentum ad ignorantiam and shifting the burden of proof.

Anyone could help me understand what I'm dealing with here, exactly?