We were told it was a 45 to 60 day wait. But we were licensed on day 44! That was the ONLY thing that happened ahead of schedule in our licensing process.
I do know that in our state if they have no available foster families, they can do emergency licenses for foster parents in your situation to take a placement. They basically put a rush on it so you can take the child.
I remember how much the waiting sucks. And it always used to annoy me when people said to just enjoy the quiet and your time with DH- but it is true! Enjoy some non-kid-friendly time!