It must depend on the keyword because in the past few weeks, I've had a couple of brand new domains hit the first page of Google very quickly. It's not for ultra competitive keywords, but it isn't for bad keywords that people aren't searching for either.
I've got well over 1,000 website that I do testing with, I'll add another 50+ this week to do some testing on.
Any particular keywords you guys want me to test? Give me something that is middle or the road, nothing too hard or easy, that way we should get some pretty quick results.