I'll add a bit of nuance to your question. The short answer is "yes", you want to get it in with AA anywhere anytime. The longer answer is it depends how, to some extent. Your question references the beginning levels of a tournament. In my experience this is where opponents will gamble the most. We should always be betting or raising with AA here and pretty much never just calling. That does not mean we should just jam all in when a few players have only called or made a smaller raise. Try raising an amount 3x or 4x the current BB pre flop, a little more if there are players already in the hand. If they raise again then you can also raise again. When the ratio of the pot to your remaining stack goes down to a level of 1.2 or lower, that is the time to move all in. It doesn't make much since to raise less at that point and have say 800 left with a pot size of 2200 for example.
Example: BB = 30, ACR on demand $10 freeroll.
UTG calls 1 BB
UTG+1 calls 1 BB,
MP raise to 3 BB (90)
CO calls 3 BB
Hero on BUT with AA (50 BB, 1500): The pot is 9.5 BB our stack is 50 BB. There is no need to shove here. Just raise to 12-15 BB (360-450) and if they raise or go all in then you can go all in.