Can I still claim my son as a dependent if he became a recruit for the U.S.Marines June 24th and graduated September 22, 2023?

Yes, moving to be in the military is the same as living at home, but he would also need to meet the other requirement of being under 24 (since he was a student) at the end of 2023 and not suppling more than half his own support. 

Graduated Boot Camp 9/22/23?  I would say "No, you cannot claim him".  He has become his own taxpaying entity and you cannot claim him any longer as a dependent.  If he is Reserve or Active duty, he is earning his own income and having his own uniform expenses...(make sure to tell him to keep his receipts for uniform replacements and out of pocket haircuts that the Marines doesn't reimburse him for).