It took almost exactly a year after applying and getting a cp rec to getting the first email. From the time I got the initial email to the time I was in class was approximately 2.5 months. I attended a job fair, had multiple internal recs. I'm a heavy mil guy mostly. I know guys that are still waiting after multiple years, and others that got the hogan invite after applying only 2 months earlier. There really is no way to know what your timeline will look like.
Good luck!