Originally posted by Owen E Oulton
"Not necessarily. IIRC, Kirk became a captain shortly after the Academy."

You recall incorrectly. Kirk stated that he became a captain at age 32. He was 34 in first season TOS, so Enterprise was almost certainly his first command. While 32 is very young, it's also 11 years after his graduation from the Academy (he entered Academy at age 17).

However, Kirk was written according to the whim of TGBOTG, not generated according to game rules, so he's hardly a valid example...
Well, all of this assumes that you have to hold the rank of Captain to hold a command. This isn't true. In the US Navy, the rank of a ship captain can be as low as Lieutenant or Lieutenant Commander depending on the size of the vessel and the mission of the vessel.

And, don't forget, Sisko took command of a whole space station as a Commander.