It's hard to say given that we have maybe 3 dates in the whole movie, but if Kirk entered the Academy at the same time that he did in the original verse, Chekov would be 5 when Kirk enters, making him 8 at the time of the movie. Even with some slippage in there, it's still -- thing.

In the whole movie, everyone's age is off even relative to each other. I kinda gave up, really. I mean, Bones should be older, I can't tell with Scotty, and again we've got that whole issue of 'straight from being a cadet.'