As far as the term "early game rush," yes it is possible to get rushed by turn 10-14 but it is incredibly rare. If you get rushed that early by 5 or 6 AI warriors your chances of survival are pretty low no matter which Civ you are playing (especially if you have sent your initial warrior scouting, which most people are going to do). Between 15 - 20 if you have been building slingers, you should have enough of them to have already killed something with a slinger and you can usually have Archery by turn 18 give or take (unless you found a Science city state, in which case you might have it faster). Once you have archery, if you have managed your money properly, you have at least 2 Pitati archers and are in very strong position.
So yea, if you got rushed by turn 12 and were playing Aztec, maybe you survive IF you keep your initial warrior in your capital and build another warrior. (So no scouting, no goodie huts, no discoveries, just turtle right from the start. Highly inefficient strategy.) Even then, you might not survive because AI is much more deadly now with their rushes. They will likely ignore your 2nd warrior and just slam all their units against your city until it falls. Plus, if they rush that early, it is likely they will keep sending an endless stream of units until either your defenses are strong enough to stop them or they take over your capital. Even if you manage to hold them off with Aztec warriors, your growth has been devastated so badly that recovering is going to be difficult.
So I don't think it is useful to focus on a turn 10-14 rush. That is going to ruin almost any game unless you got extreme luck with chocolate/gems and some commercial city states and can just purchase an army right from the start. Vast majority of early game rushes are going to be around turns 20 - 30.