Lots of the constants just come from the (best current knowledge) maths looking at things as they are now.
e.g. If I had lifespan equivalent to the universe, If I was "sampled" in the human era, things like my waistline, blood pressure, time to run 100m etc would be a lot worse than when I was in my prime (which, on universe timescales would be billions of years earlier), but my current stats would appear constant over the (relatively tiny) timescale used.
Querying constants is nothing new, there's always been people asking "how do we know this constant has always had this value"
.. I remember, as an inquisitive / PITA schoolkid (delete per your preference) asking my physics teacher that at comprehensive (forgotten which constant my question was referring to, might not have been c) and getting the (honest) answer of "we don't".
A huge amount of our physics knowledge is just best guess theories, there's a long way to go before we can really explain the universe with any half decent chance of accuracy.
Theres so many ideas being proposed in theoretical physics (TP), it only tends to be odd one or two that get much media attention though.
It's very difficult / impossible to experimentally prove / disprove an awful lot of TP stuff, so it's an ideas churning out industry (though at least this is potentially disproveable)
Disclosure: I studied some physics / astrophyics to university level but do not work in physics, but I still have an interest & read about the subject (instead of grappling against a crossword setter, try and pit my old addled brain against some hard maths & odd concepts)