Months
Josh,
Depending on the keywords it could take months. Also the big G loves to "sandbox" new sites after a few weeks. You can look up that term "Google sandbox effect".
I have a site that keeps bouncing from the top of page one to page two almost ever day.
You have to think long term with Google SERP. Keep adding some content and links. Also try to get links that will stay in place for a long period of time. That helps your SERP IMHO.