You are eligible to apply from the day you report to boot camp, Your recruiter is misinformed. Military citizenship is prioritized over regular applications for naturalization. USCIS has a dedicated group in Nebraska that process military cases exclusively. Once you report to bootcamp, let your seargent/whatever know that you wish to start your process for naturalization. At least in the Navy, I have known people who received their citizenship by the time they graduate out of bootcamp (8-11 weeks).