How many minutes between jetway (air bridge) detachment and take-off?
while I don't think such a regulatory minimum would make sense, I'm still curious about whether it exists.


No, there is no such regulatory minimum.

On average, it's between 10 and 20 minutes from pushback to takeoff, although there are a couple of places I can think of (very short taxi from gate to runway) that I've seen it done in under five minutes.  That's moving pretty fast, though -- almost nonstop checklists, other than during the time the engines are starting.  But whatever you can do safely, is fine as far as regulations are concerned.  If you're ready to go, no regulation makes you wait.

Depending on the aircraft, there may be an engine warmup requirement or recommendation.  That's typically much more restrictive for the first flight of the day, and that would be a limiting factor in the very short taxi cases.