Correct. The thing we don't know is if he was immediately promoted to captain as well, or was only promoted to commander, then captain after he proved his competency/excellence over a period of time.
Ugh, I think you guys all read memory alpha too much.
There really are no established dates for any of that stuff. It's all just conjecture on a single line of dialog where Q said that without ambition Picard never would have taken charge of "the Stargazer's bridge when its captain was killed." All this "2233" or 22 years stuff from all that I can tell is just made up.