To get from lieutenant on the Farragut to captain of the Enterprise in eight years, if we accept that Kirk was the youngest captain in Starfleet history, does seem doable. But is it doable to insert another command of another ship in there? That's what I was discussing, whether he had time to have served a tour as captain of ANOTHER ship before getting the Enterprise.
Why in the world wouldn't he? It's eight whole years. Riker was a lieutenant in 2361 and a commander getting offered his first captaincy only three years later, and he served on at least two different ships in that three-year span, the Potemkin
and the Hood
From what I can tell in a cursory Google search, in reality a typical military tour of duty at a single posting can be anywhere from 6 months to 3 years. Heck, in real life a Navy captain would only command a ship for maybe 6-18 months before being rotated out and replaced with a new captain. The WWII-era USS Enterprise
CV-6 was in active service for eight years, in which time it had twelve different captains
, not counting the commander who was its CO during repairs at Pearl Harbor in July 1944. (That's right -- a ship in port can have a different commanding officer than it does when it's in service. After all, the captains would be needed elsewhere.)
So eight years is, yes, absolutely, plenty of time for Kirk to rise from lieutenant to captain and have at least one command posting. (And TMoST said that Kirk was at commander's rank when he got his first starship command, a destroyer equivalent.)