"Fast enough" is very nearly orbital speed, though. Suborbital range is very short on the lower end, and increases rapidly and nonlinearly later. E.g. if you can boost to 2km/s (~ Mach 7), this gives you, I kid you not, around 200km of ballistic range. It's either atmospheric flight or orbital flight, and there's nothing really useful in between.
But judging by "in four hours" I'm guessing he's imagining something somewhere in between those two extremes. High enough to substantially reduce drag, low enough that you don't need to approach orbital velocity to maintain altitude.