What this says may not be relevant in your case, but according to the 7th Army Training Command Legal Assistance Information Soldiers’ Naturalization Checklist, " In most cases, the earliest you can submit your application is during basic training".
If you can get it done before Basic, then that's wonderful! And congratulations both on soon to be citizenship as well as military service. The military is like home to me, and current and past members feel like extended family. I served in the Army on active duty and then the Army Reserve. And now I am blessed to be a part of that community all over again, through my wife who is serving in the Air Force on active duty. She started out her career by first serving in the Tennessee Air National Guard. Take advantage of every opportunity you get, and embrace it, and most of all enjoy it. Best wishes to you in all your future endeavors.