My wife is foreign-born, but was in the US as a non-resident when our hearts turned proximity into much more. Since she was already here the whole application process took place in the US. It was just under two years from when we married until she had a green card. (And note that there is also a delay from being granted a green card to actually having one in one's possession.)

Foreign passport and non-driver's ID were her only options--and passports are a nuisance to carry around and a PITA if lost/stolen.

(And, yes, I think that just under two years bit was not by chance. They were definitely looking for signs of fraud and I'm sure they finally approved it just before the point where they would have had to issue a permanent one rather than a conditional one.)