A rocket motor needs liquid propellant at best, so no. So like a jet engine first stage? A Falcon 9 is already 40 miles up in less than two minutes. Your jet first stage would maybe be able to get the rocket to 40,000 feet before rockets have to take over, so maybe some tens of seconds of flight. And then we have size/weight issues. Our most powerful jet engine is the GE9X at 110,000 lbs thrust. You'd need several of these to replace rockets, and they're huge and heavy.

The best idea we have so far is to haul a rocket up high on a jet airplane and then launch it, but that only works for smaller rockets.