There’s also nothing that indicates Kirk didn’t serve on the Enterprise in another role before getting promoted
Hm, here’s an interesting formulation for all or part of a final season:
Pike leaves, becomes an Academy instructor
Una becomes captain of the Enterprise
Kirk transfers in to be her XO
Kirk and Spock working together for a year or so would give us a chance to explain the unusual situation where Spock is simultaneously science officer and XO. By the end of this season you’d have the full TOS crew in place. (Minus perhaps Chekov, or maybe he’s a cadet like Uhura was in season 1.)