Spock met Kirk when he (Kirk) assumed command of the Enterprise. Kirk was in his early thirties between 30-34 (another subject for another discussion). He would have had access to Kirk's record and Spock has excellent memory recall. He would know exactly what Kirk would look like. If kirk looked noticeably younger (to Spock's eyes) he would know he couldn't have been in command of the Enterprise.
And while this is out of universe photos of Shatner a mere five or so years before Star Trek show a noticeable difference even to human eyes.
We don't know when Prime Kirk and Spock met. At all. Your assumptions
say they didn't meet until TOS, nothing more.
Same for Kirk's age when he became captain of the Enterprise, or even achieved the rank of captain - he may even have commanded another ship prior to the E. He may also have commanded the E for a time before the 5YM began.
Up next: It's an alternate universe because Chis Pine's hair is real.