There's no minimum age as far as I'm aware. However, with auto-promotion ranks are based on how many officers are in the previous rank (IE if you have 5 captains and 0 commodores, one captain gets promoted into a commodore). So if you have the same amount of academies you'll likely end up with the same amount of naval officers, and therefor the same amount of rear admirals, only getting replaced as the previous ones retire/die.