Not really though? Non-existence of anything is the default. Existence of something puts the burden of proof on whoever claims this something exists. "Quantum mechanics" is a bad example, it's a set of theories, not a single theory (like "a god exists"). Depending on what is being claimed, you can easily show people papers, such as this one which shows experimental observable proof of principles of quantum theory.

At one point, quantum mechanics didn't exist and wasn't generally accepted. Physicists like Heisenberg took upon them the burden of proof and provided it.

General acceptance is how it is treated since then, by non-physicists, but it is simply possible to follow the proof of it if you really wanted to. There are experiments that have been performed and that can be performed again that create observable evidence of the principles of quantum mechanics.

The burden of proof still lies on proponents of quantum mechanics. What you're talking about is more of a societal shortcut, accepting that the burden of proof has been verified by other people, not by yourself, as it's impossible to go deep enough into every subject to actually verify every proof you come across. That's why specialization exists.

The difference is that 99% of physicists confirm the proof of quantum mechanics. Specialists on religion are all very much divided on which god(s) or whether at all one exists, and no proof exists for any religious theories.