I don't think it's unreasonable at all for Starfleet to assign a Constitution-class ship to one of its most capable up and coming officers, especially if that officer has proven himself/herself as a leader ever since graduating from the Academy.
But where would he have proven himself a leader? What would he have commanded? There is a vast difference of responsibility between being a department head or even XO of a vessel and being the actual honcho. Unless he commanded some very important "ground" expedition or something I think it's fairly unlikely Kirk would have the applicable experience to get a cruiser as captain without a previous smaller vessel command.
If Starfleet has vessels smaller than Enterprise
it would make little sense to select commanders of bigger vessels from officers other than those who had commanded a smaller vessel. Especially a one-of-twelve, pride-of-the fleet type of command. If there are destroyers, scouts, frigates, corvettes or whatever you will, where are their former COs going if not on to larger commands? It would be a waste of experience. Such has been the pattern of naval command from the days of sail, with exceptions in the last half-century with the sharp reduction of captains' commands in warships.
I admit I am making some assumptions, though. There is not much onscreen evidence for smaller Strafleet ships, and if they exist I suppose their numbers could be even fewer than the cruisers, which would change things.
Kirk may have leapfrogged over some more experienced people, but such things happen in every occupation.
It doesn't happen too often in military organizations. You don't find many captain-grade warship COs in their first command, or brigade commanders who never commanded a battalion, or wing commanders who never commanded a squadron.
I agree that there's nothing onscreen that confirms either way, but I think an educated guess weighs toward Kirk having commanded a vessel before Enterprise