That said: Big Bang does explain an awful lot of stuff. I'm not sure what JWST observations you say call it into question, but wouldn't we need a lot more data before advancing Big Bounce or something else as an alternative?
The JSWT observations putting some doubt on the Big Bang theory are the observations of very old galaxies. E.g. one was observed at a time that the universe was only 250 million years old (according to BB theory), really not much on a cosmological time scale. The thing about this galaxy was, that it seemed like a pretty normal galaxy already. Which makes people wonder how it could have formed so quickly.
Another observation casting doubt on the Big Bang theory is the (indirect) observation of some very early massive black holes. Again the question is how they could have formed so fast.
There is no other plausible explanation of the cosmic microwave background radiation.
I like speculativity very much, it's just a note on it.
But anyway, give an alternative model that explains it. I'll wait.
There are some alternatives to the Big Bang theory, e.g. the Big Bounce. This also claims the existence of a thick hot early state, but a bit more than a single point. This theory also explains cosmic background radiation.
> The BB is compatible with inflation, but theories of inflation were proposed well after the BB theory itself.
Exactly, and the reason these theories were proposed was to 'fix' the BB itself. So of course they are compatible with the BB. There is no observation that asks us to consider something like hyper inflation, except if you assume that there has been a BB.
Empirical Science is about building theories based on observations. We have no observations that provide any kind of evidence that there was a big bang. Yes, we now that the universe is expanding, and has been for quite a while. So reasoning backwards, there must have been a time that the universe was a lot smaller than now. But that's it. We don't know how small it was before it started expanding. Maybe our universe started from a single point or even from nothing. Or maybe it bounced back after having contracted to a small but definite size. We just don't know. And actually, with the recent JWST observations, hints that support a big bounce or something similar are building up.