He tells La’an about Carol when they meet for the first time (well for him it’s the first time) So they’ve been together for a bit. Maybe since the Academy? I don’t think the blonde lab tech has officially be said to be Carol.Yeah, ummm ... Jim & Carol would apparently have happened either while he was at the Academy or just after him graduating in the TOS timeline.
Gary Mitchell is supposedly been the one to have introduced them to each other.
(and we haven't even seen him in SNW yet)
We may have to adjust the year of that event, Kirk has only been shown as the Captain of the USS Farragut in the alternate timeline so far and he's still a Lt. as of Season 2.
The Farragut Captain Kirk would be from a time equivalent to Season One TOS.