I don't think so. TOS did strive for a measure of realism and it doesn't make sense that an organization will hand one of its prized ships to a neophyte. Note that all other ship commanders seen in TOS were older and experienced men. Kirk would have to be tested and proven to be given such a prized command, not a lucky dumbass like nuKirk in ST09.That's incorrect. Or rather, it's your opinion given that there's no onscreen material to support it.Incorrect. In the character's bio reprinted in The Making Of Star Trek it says Kirk commanded a destroyer equivalent class starship. This is reinforced by a reference in WNMHGB when Elizabeth Dehner metioning Kirk having asked for Mitchell aboard his first command.As far as onscreen material goes, there's no mention of Kirk commanding any other ship prior to the Enterprise.
For starters, it doesn't matter if it comes from a book if it doesn't make it onscreen (fans of various reference books written by people who worked on Trek know this very well). Secondly, Dehner's comment doesn't preclude that Kirk's first command was the Enterprise and that Kirk wanted Mitchell to be there with him. So it could go either way--either Kirk was captain of a ship prior to the Enterprise or he wasn't--as there is no way to prove either position from onscreen material.
The only answer to the question in the OP is that there is no official answer, only our personal conjecture and opinions.
Whats in "the book" is a reprint of the character's bio from the Writer's Guide which was handed to those who wrote for the show. Sometimes they deviated from it, but in this they didn't and the spoken reference from WNMHGB is consistent with it. Since it was never contradicted later on then it seems to be pretty established. And it makes more sense than any bullshit similar to what they did in ST09.
And just because Kirk asked for Mitchell aboard "his first command" doesn't mean he got him. Maybe when he was given the Enterprise he had a little more pull to get an officer he wanted posted to his new ship.