Think of the Kelvin Timeline as another Mirror Universe. It’s always been there, always been different, it just so happens that our Spock got stuck there.

As for the lead not being a Captain, there’s a lot of possibilities there. From what I understand, The West Wing started out focusing on everyone but the President. Or think of “Lower Decks” or similar episodes, which explored what life was like for non-senior staff members, which could make for an interesting series. Or the senior staff is wiped out in the first 10 minutes and she’s the highest ranking person on board.