We do have reason to believe he had a long career as an instructor, what with the reference to "Lieutenant Kirk" teaching Mitchell, and Kirk not leaving the Academy until under the command of Garrovick Sr. on the Farragut
. Aboard that ship, he did encounter a high-casualty situation he himself survived just fine - the massacre described in "Obsession". Perhaps this was a crucial step in elevating him in rank and prestige, as well as associating him with the ability to navigate a heavy cruiser through a serious crisis - leading to Starfleet giving him command of the sister ship of the Farragut
I mean, it's far from impossible that Kirk would have gotten the Enterprise
straight from Pike back in 2257 already. Pike might have taken Spock with him for the rest of their quoted joint eleven years, thus explaining why Spock and Kirk aren't the closest of pals in "Where No Man" yet - Spock returned to the ship and joined Kirk's crew only shortly before the episode. And Mitchell would be with Pike as well, explaining why he and Spock are close colleagues in Dehner's opinion.
Or then Kirk got the ship from Pike, but only after serving under him on the Enterprise
for some time, again leaving no in-between ship for him to command but a direct progression up the ladder in the close-knit Constitution