How long it takes for new cryptographic results to become generally accepted? Suppose there is a new scheme, for the sake of argument let's call it a CEPQSS - CryptoEnthusiast's Post-Quantum Signature Scheme. Now most practitioners aren't convinced that using this is a good idea let alone that it works. But the results are completely valid.
How long would it take until most practitioners evaluate and peer review it to the point where it would be generally accepted?
How long would it take until most practitioners evaluate and peer review it [...]?

Unfortunately peer review tends to be more of a &quot;push&quot; than a &quot;pull&quot; based process. Meaning that experts in that area tend not to crawl the internet for schemes to investigate and &quot;declare good to use&quot; but rather that the authors of such schemes work hard to get that attention. And even then, most schemes - even those with somewhat famous authors - have excellent chances at never being used seriously in practice. This is the case even if the relevant people have used much of their time to analyse such proposals and found no flaws.
The best example for this is actually the on-going NIST Post-Quantum Competition where chances are really slim for any candidate kicked out in the third round to see any real usage.
So even if a scheme is good - and it has to be reasonably secure and performant - and it is published in the right place at the right time with a large amount of serious, convincing self-analysis, there's a good chance that it never sees real usage outside of that the author implements themself.
This situation doesn't get better if the scheme in question has no properly formatted paper with lots of relevant, convincing cryptanalysis and security proofs, which hasn't even been submitted / accepted at the right venue / journal.
If one would really want to have such initial analysis it might be worth to try and hire a serious, professional cryptographer as a consultant and either have them analyse the scheme - which is unlikely to be very useful given that this kind of work takes a lot of time and thus money - or to collect (some) likely relevant initial background material to start working on the analysis in a way that is generally accepted. Additionally such professional help would likely also be able to review the analysis to give potential improvement suggestions to the analysis and its presentation to lessen the chance of an instant reject if and when it is tried to be submitted to a serious venue.