Back in 3, you could build a settler every 4 turns on a good start, and usually could get a settler every 6 turns.
Well, I guess it depends on the speed of the game you're playing - I tend to play longer games, where 4 turns for a Settler anywhere before the Industrial era is just crazy talk.
EDIT: But this isn't to say you can't expand quickly - I just think the pace you're suggesting is somewhat ridiculous. I also like to sprawl, and there's a social policy tree to sprawl quicker, and a social policy tree later on that rewards having sprawl, Liberty and Order, respectively. Liberty can get you a free Settler and speed up Settler construction in your capital. It also depends on the civ you're playing - Polynesia is particularly good at sprawl, since it can just hop over to islands immediately. In that case, I would definitely recommend Commerce, since you can get extra production in coastal cities from it.
EDIT2: If you like, we could multiplayer sometime - not to brag, but I consider myself more of a challenge than the AI.
Though the AI has also been improved in the expansion, and apparently more so in this upcoming one.