[handsaway]

Assuming you mean "Big Bang" in the sense of the beginning of the universe, not necessarily.

>doesn't the fact that the Big Bang happened imply that there was some kind of state-change: from Big Bang is not happening to Big Bang is happening

Language is incredibly bad at describing this because we did not develop it when such a concept as "outside of time" existed. The word "happened" is misleading you I think. If we define "something that happened" as an event with a before and after then the Big Bang did not, by that definition, "happen".

I've had it explained to me that asking "What happened before the big bang?" is akin to asking "What's north of the north pole?"