Would it take a big object to start it spinning, or would any glancing collision just start it spinning a little, and with no atmospheric drag would it keep going?
I may not be understanding the OP correctly but, if so, I’d add that the Moon is in fact rotating but it’s rotation rate is the same and it’s rate of revolution around the Earth so we see the same side all the time. I seem to remember that the same is true of the planet Mercury in that one side always faces the Sun.
Are you asking if the rate could be incresed by a blow to the Moon to allow the face to change?
Nitpick: It’s now known that Mercury doesn’t always have one side face the sun. But it does rotate three times for every two revolutions around the sun, so every two revolutions it’s back to where it began.
In principle an impact could add extra spin to the moon but in practice the moon would be severely disrupted or even fragmented by any collision with enough energy to measurably change it’s spin rate. Most of the momentum of an impact would go into the debris knocked loose.