The army giving out LOA's is totally irrelevant. They've given out LOA's to individuals who haven't even started the application process yet. It's their way. As for the Navy and LOA's, I'm not sure how they do theirs.
As for the Navy giving out "APPOINTMENTS" already, I can tell you right now, that the ONLY way they've given out APPOINTMENTS, is if those individuals received a Military Related Nomination, such as a presidential, ROTC, MOH, etc. Because, in order to receive an APPOINTMENT, you MUST have a nomination. (Except for the coast guard academy). And MOC's in most places haven't even interviewed yet. Most MOC's won't give out their nominations until at least November.
As for the Air Force...... I do believe they have started the application review boards. But don't hold your breath for any appointments to come out any time soon. They MIGHT offer some LOA's; usually to athletes, if they are a "TRUE" recruited athlete. VERY COMPETITIVE and sought after by many other schools. (Not like the 90% who are called recruited athletes by name only). It's also true that the air force could give out some appointments. But if they do, as I mentioned with Navy, they would have to go to someone with a MILITARY RELATED Nomination. Because MOC's haven't done that yet, and you must have a nomination in order to get an appointment. And if there are a couple of appointments to some with a military nomination, I can guarantee you that those individuals will most likely be part of the "No-Brainer Club". Meaning, they are above the top 10%. They're above or in the top 1%. These are usually individuals who in the end, will have acceptance letters, and probably scholarships to no less than 5 schools. If you're not sure of the "No-Brainer Club", it's the applicant with the 4.0gpa in the HIGHEST CLASSES available; 32+ACT, class officer, ranked #1 or #2 in the class; 2-3 varsity sports, captain of the team, honor society, numerous other clubs, boy/girl state, 200-300 hours volunteer time, bla bla bla. So, if there will be any appointments now, it's these individuals who ALSO HAVE A Presidential or ROTC or MOH or other military related nomination. This is a rare combination.
Other than that, the first REAL ROUND of appointments will probably be the beginning of January. It depends when the MOC's get their nominations submitted. Obviously, if a MOC gives a Principal nomination, the academy can give the appointment that same day. Because, unless that individual isn't qualified, the academy has no choice. They MUST give that individual an appointment. But other than those few exceptions I've mentioned, look for January. And I will say the same thing about the Navy and Army. They can't give out appointments without nominations. So unless an individual has a Military Related nomination, and is part of the No-Brainer Club, they probably won't be sending out any "WAVE" of appointments until after November, when most MOC's interview and start giving nominations.,