You seem to be missing the point of what I said in the reverse direction. It was never established that Jack Crusher was as old as Picard as before, and the implication was always he was a bit younger if he served under Picard in the Stargazer, roughly the same age as Beverly.To be fair, you can attend the academy at any age. See McCoy and Vulcans.
He's said to be about 24, which means he's older for his age but not that young.
Even if Jack started Academy at 13 years old like Kelvin Chekov (assuning Kelvin Chekov took 4 years) and immediately hung out with upperclassman Picard, he'd still be 11 years older than Beverly.
If Jack is 23 or 24, that'd put his birth between Insurrection and Nemesis. I mean if you take the exact words of Picard dialogue you could probably forcibly fit this somehow but the entire seeming intention of the circumstances of Jack's birth seemingly put it after Nemesis and it stretches plausibility to the extreme that Beverly hid a pregnancy and then Jack's birth and then the infant himself between Insurrection and Nemesis.