I think you are taking proof as a word too literally and conflating it with different notions of proof (formal and informal). You should really find a comprehensive book on the Methodology of Science itself if interested or there may even be online resources.
Many colleges will have courses and material. For example
http://logic.berkeley.edu/
is a fantastic and very useful program.
I have already mentioned earlier the various stages of how discovery progresses in science - from conjecture to hypothesis to theory to law of nature (in physical sciences).
The method of science requires certain rigor in establishing what people (to be exact peers) would accept to go from just a conjecture to a theory to be classified as a natural law. Typically, this uses one or more of empirical evidence, experimentation, observation, deduction or a logical inference, etc.
The default for science for some X is unknown/unproven, not some Y unless there is a counter-example. And there can be more than one conflicting theory or hypothesis at any time unless one of them can be rigorously invalidated.
If you propose a Y, then it would be contingent on you to make the case for Y including one or more of the above. That includes, why another plausible Z isn't the case. The thing that can trip these logical line of thought to advance a theory is incomplete logic or some aspect of it can be shown to be demonstrably false or has a false premise. This is why detailing the whole argument is important and peer review of that whole argument is so important.
In lawyering as a contrast (which is what most Internet "science" brandishing is about), the goal is to prevail not find the truth (except as it may be coincidental) which can include incomplete or incorrect logic as long as those remain persuadable (or the opposing lawyer or jury didn't catch it). In science, that would be discouraged and a show-stopper.
Here is an example of incomplete argument:
Conjecture: A human being cannot distinguish between two DACs that have SINADs above 100db
Argument: We have studies that show with statistical significance that humans cannot hear noise below that level. Therefore, it is impossible for human beings to differentiate between those two DACs with measurements above 100db
A possible objection from a peer review:
The argument is true but incomplete for the thesis. The problem is people are listening to some content presumably in stereo and you are making a claim for this scenario. What if the channels of a DAC were not in balance and one of them showed a perceptible tilt to right or left. People would be able to differentiate between that one and another that didn't have the problem, right?
Reply to the objection:
But we fix all of those issues to ensure that both DACs have the same levels and that they have the same channel balance.
Peer objection: But you didn't explicitly specify channel balance as part of the argument. What other parameters are also fixed that would otherwise affect the perception. Do you have confidence that you have caught all possible parameters? If so, you would need to provide an argument to establish this. Otherwise, the argument is incomplete.
Etc. This is just a start.
So if you were to go through this rigor of scientific peer review, the list I posted earlier of what you would need to show to be is what would be acceptable for such a peer review. So that a theory can be advanced and accepted as a plausible theory. Nobody has really done this for this specific issue (this is different from there being multiple controlled studies on various things). Because, it is polarized into two groups - one who believe with no evidence that passes scientific rigor that they can hear a difference and another group that is fully convinced that is the case without actually constructing the entire argument and having it checked for validity (not agreement within an echo chamber or similarly convinced people). Until then, neither side has really "proved" their case.
Note that I am not saying that such a view is wrong, just that it has not been established to a rigor (evidence, studies, limits, assumptions, caveats, relation to alternate theories, etc., that directly deal with the hypothesis of interest) from which it is possible to say "science shows...".
There is no such thing as "persuasive evidence" in science.
The rigorous method of science leads to an effective vaccine. Persuasive evidence leads to accepting hydroxychloroquine as a solution. That is the difference.
We should be glad we have the rigor of science as a common basis for such research. Anyone who is in the scientific field and has gone through it to a higher level of studies gets exposed to and fully understands what that involves, a lot of it from simply the difficulty of getting papers peer-reviewed and accepted. So, the Internet argument nonsense typically does not happen there.
It is unfortunate that this rigorous methodology (including what constitutes a controlled experiment, what is valid logic, what constitutes a logical argument, etc) is not taught much earlier. This would avoid much of the misuse of "Science" whether it is in audio, or climate issues or any of the many problems facing the world today where people misuse "science" simply to advance their convictions (which as we know are subject to multiple biases).