The pilot told the Crew Chief via intercom "Engage Buicks". The Buick operator pressed "Jet Start", and movement of the Buick throttle (one throttle lever controls both engines) downward engaged the transmissions. . . . The pilot would watch his onboard gauges to confirm minimum oil pressure, fuel pressure, and rising RPM, and then set the jet throttle to idle. At that point 30cc of TEB was injected into the burner cans, a characteristic green flame was emitted, the J58 lit off, accelerated and started to run on its own. The accelerating jet started to unload the Buicks, and when 3,200 rpm was reached, the pilot called "Buicks out", the Crew Chief signaled "cut", the Buick operator hit "Cart Shutdown", the probe fell free passively, and the cart throttle automatically returned to idle.
https://www.thesr71blackbird.com/Aircraft/Engines/starting-t...
So the gist of the idea is not that far fetched.
(Now I'm wondering how the huge Diesel engines on massive boats are being started, I wouldn't be surprised if they were started by a smaller IC engine)