Running one pack isn't in the same league as starting an engine...
Engine start is a 'transient' phase, with a truck load of power at the start which usually dies away as the engine spins up.
Engine start from ground power involves load shedding loads of other less critical electrical services.
Pack operation (I'm guessing 1 pack from 1 CAC? Never done this myself!) is a constant high electrical load - Just look at the decrease in fuel flow when you have a CAC fail...