Mendez is clearly using Kirks previous meeting of Pike as an anchor point for his description of the man. Pike was about Kirks current age (within 5 years) when they met at his promotion. The rest of his description concerns past Pike as well.
One problemwiht tha theory is that Kirk was captain of hte Enteprise for probably a relatively short period before "The Menagerie".
I calculated the possible time span elsewhere.. But finding that might take more time that writing another discussion.
In "The Menagerie Part 1":
MENDEZ: You ever met Chris Pike?
KIRK: When he was promoted to Fleet Captain.
MENDEZ: About your age. Big, handsome man, vital, active.
KIRK: I took over the Enterprise from him. Spock served with him for several years.
SPOCK: Eleven years, four months, five days.
And when the transmission from Talos IV begins:
SPOCK: This is thirteen years ago. The Enterprise and its commander, Captain Christopher Pike.
So assuming that Spock began serving with PIke at the tiem of the Talos IV incident, and that tirteen years is between 13.0 and 14.0 and estimating that "Eleven years, four months, five days' is approximately 11.347022 Earth years, the moment when Kirk took commandof the Enterpise should have been 1.652978 to 2.652978 years before The Menagerie Part 1".
Soif PIke was then 6.652978 to 7.652978 older than Kirk, he wold still have been a very young commander of th e Enterprise at the timeof Talos IV, and would have gained command much younger than Kirk gained command.
Maybe Spock started serving under Pike some time before the Talos IV incident, For each year that Spock served with PIke before the Talos IV incidnt, the date range when KIrk could have become commander of the Enterprise would be one one year earlier.
However, the age of Spock's mother Amanda in"Journey to Babel" makes Spock's position of third in command at the time of Talos IV seem like he was very precocious, or Amanda ws a very young mother, or both. So maybe it is not a good idea to begin Spock's starfleet career any earlier than necessary.
Everyone tends to assume that "When he was promoted to Fleet Captain." and "I took over the Enterprise from him." refer to the same evnet, but maybe they don't. Maybe Pike retained command of the Enterprise for several years after being promoted to fleet captain, and so the last few years of Spock's service with PIke could be after the one time when Kirk met PIke - since Pike might not have been present for the ceremony of transferring command to KIrk.
And of coursemMaybe Pike was more than about five years older than KIrk. Maybe Pike was 10 to 15 years older than KIrk, and maybe Mendez thought that was not a big difference in age compared to his age, and maybe Mendez was rmembering PIke from sometime before the time when Kirk met PIke,
So those seem to be the possibillities.