simple QQ level 1

Damn, I read the result again.

Anyway, I think nobody'd argue that his hand range is something like TT+, AQ+, possibly looser, possibly tighter. You're a 55/45 favorite against this range. If the flop comes down with an A you're a 35/65 dog. An A and no Q will flop about 19% of the time (this is a high estimate because our opponent is more likely to have an A than normal). So, if we call and assume our opponent will push when checked to (or bet less and call if you push), we should fold about 19% of the time, in which case we're left with 650. The other 81%, we're going all in as a roughly 70/30 favorite (this is a very low estimate), giving us about .7*1625 = 1138 cEV.

So, the cEV on the call/check/raise play is about .19*650 + .81*1138 = 1045. The cEV on pushing preflop is about .55*1625 = 894. So, the call/check/raise play is much better given the assumptions that I've made which are 1) the villain's range and 2) that the villain's not folding.

If you add more hands without aces to the villains range (more PPs, KQ, KJ), pushing becomes the smarter option. If villain will check it down with a PP after an A falls, the call/check/raise play becomes better. If villain will fold a PP to your push after a K falls, the play becomes worse.

In general, though, I think that seeing a flop is by far your best option. Keep in mind that this play is not only likely to be +cEV, it also lowers the variance of your stack size in different outcomes (because you now keep 650 19% of the time). This is very good for SnGs where increasing your stack isn't as important as keeping it.