How does the Blackbird SR-71 pressurize the cockpit at Mach 3?
The SR-71 used the P&amp;W J58, which is full of moving parts, and works very similar to a typical jet engine.  Your assumption that it has no moving parts is wrong.   While the engine RPM did slow down at maximum speed (up to 90%), it never stopped, and always generated enough power for electrical systems, pressurization, hydraulics and any other needs.

While the cockpit was pressurized (but sometimes only to 26,000 ft. pressure-altitude), the two-man flight crew wore full body flight suits for warmth and oxygen.