Incidently, I was thinking of a turbopump "start-up" system
involving...
(1) A 'disposable' electric-motor inserted in the launch-pad beneath the 1'st stage rocket-motor.

(2) A rotary-transmission rod from the electric-motor would have a screwdriver-like head inserted into a slot in the bottom "hub" of the turbopump.
(The rotary-transmission rod would have a passing resemblance to
a humungously oversized screwdriver)

(3) The electric motor revs up, transmitting rotational-energy
to the turbopump until sufficent RPM is achieved prior to rocket-motor
ignition...

(4) Once the I'st stage rocket motor has achieved sufficient thrust,
the "siphoned-off" hot gases can then sustain the turbopump's RPM.

(5) And FINALLY the rotary-transmission rod is yanked out of the turbopump's hub and then recessed back down into the launchpad to keep it out of the way of the rocket-motor's components as the rocket lifts off.

Are there drawbacks to this idea?
Certainly!...You could only use it on the launch-pad and only on
the I'st stage turbopump(s).
And the electric-motor would be written-off after only ONE use,
unless it's well-shielded/insulated from the rocket-motor's blast.

Jacob

"We choose to go to the moon, and do those OTHER THINGS, not because they are easy, but because they are hard."
John F. Kennedy