we're talking about a sequel to a film where a character went from cadet to captain in a matter of weeks/months.
Rapid career progression is my main beef with the film.
There are those here on the forum who believe that Kirk was actually a Lieutenant based on his name being "Lt Kirk" on a console, but I don't find that plausible. He spent three years at the academy (2255-2258). Even assuming he had the credits to graduate, he would be an Ensign. McCoy would be the only one who would have graduated to a higher commission, as is typical today when doctors/nurses/lawyers/etc enter the Army/Navy/etc.
We assume the rest of the cadets were already 2nd year cadets when Kirk got on the shuttlecraft (already in uniform) in Iowa, but that would also make McCoy a 3rd year cadet at the time of the Narada incident. He appeared to be fresh off the boat.