Of current NFL coaches I'd consider elite (or close), Belichick was fired by the Browns, Pete Carroll was fired by the Jets and the Patriots, and the Eagles fired Andy Reid (although that was after a long pretty successful run, so likely a different situation). I'm not sure I'd consider any coach in the NBA besides Pop and Kerr elite (neither of whom have been fired) but Budenholzer, Rivers and Carlisle are all active coaches who won a championship after being fired earlier in their careers. In MLB, Francona and Baker come to mind. I agree more on the college ranks, in cbb Calipari was fired in the NBA, but not in college and in cfb there's the Alabama reclamation projects (Sarkisian, Kiffin) who have pretty good jobs now, but not elite coaches.

Not saying he's going to be elite, but there's plenty of precedent