McCoy: Already has civilian experience so after his Academy training his rank is proportional to his experience.
Sulu and Chekov: Already are graduates from a previous class.
Kirk and Uhura:Still cadets (have not graduated) but I explain their Lt. ranks as them taking an "advanced" track at the academy for command, where they are commissioned as Lt whereas all cadets who take the "normal" track are commissioned as ensigns. This is all fictional though and things are much different in the real world.
Too bad people (Trekkies) who frequent this forum never make that connection.