Cadet to Captain in a day.
Pretty ridiculous.
Cadet to Captain in 3 years.
Pretty believable.
Not really.
Kirk implied he'd graduate the academy in three years. Assuming he would've been cleared for cheating on the Kobyashi Maru terst -and Trek history tells us he would have been for "original thinking" Kirk would've likely graduated that year - as an Ensign.
To jump several promotions directly to captain, and not only that captain of the "flagship" (as stated by Pike) and not only
that Captain of the flagship by
bumping a distinguished, respected and vastly more experienced officer (Pike) is pretty damn fantastic.
I love this movie, I do, but really this whole idea reeks of implausibility.
It wouldn't have changed a thing to after Kirk's decoration ceremony to flashforward five years after Pike's mission and then have Kirk take over command (of course this would need an explanation for Spock's non promotion, but even TOS needs to explain that) when Pike retires/after his accident.
At least then Kirk would be around the "right age" to take command of the ship, plausibly.
It would've been more logical and made more sense and even a bit more "in line" with established history.
As it is, we've got a kid running the ship with a far too young captain.