How long does a USAF DEP discharge take?

I was recently in the USAF delayed entry program for only a month i decided that i wanted to be dropped because i wanted to enlist with Marines. My AF recruiter told me i was discharged and free to enlist with another branch when i went to enlist with the Marines they told me i was still in the AF dep. I found out i need a discharge letter, how long would it take for me to get one if i never had a ship date??