Once again: We don't know when Kirk Prime became Enterprise captain, or captain of another ship.
There you're wrong. Because as many people have done you can extrapolate from the background references in TOS. I've done it. Lots of others have as well.
- when you consider how long Spock served with Pike.
- when you consider "The Cage" happening 13 years before "The Menagerie" two-parter.
- when you consider that Kirk says he met Pike once when he accepted command of the Enterprise
- when you consider Kirk's references to the Academy, the Republic
, the Farragut
, Tarsus IV, his experience on Neural.
- the details of Kirk's background given the Writer's Guide.
- that TOS tried to depict Starfleet in a credible manner (and thus wouldn't give command of one of its frontline ships to an untested, inexperienced and unworthy person like was done in ST09)
When you put all that together you conclude he can't have gotten the Enterprise
before he was thirty and arguably later if you interpret the references sprinkled throughout the series a bit differently.