Back of envelope calculation:

  A. Starting height = 39045 m
  B. Desired speed = 343 m/s
  C. Acceleration = 9.8 m/s/s

  D. Average speed while accelerating = 171 m/s (half of B)
  E. Time to reach desired speed = 35 s (B divided by C)
  F. Therefore distance travelled = 5985 m (D times E)

  G. Therefore altitude at Mach 1 = 33060 m, give or take the small amount of drag.

Edit: Meh, I see from the video that he didn't accelerate as fast as this, I guess the drag was significant after all. Even a small amount of gas will move you if it's coming at you at significant speeds...

I think he meant altitude at which he was slowed back to mach 1.0.