Ok, so Kirk was very young when the car went over the casm. But he was older when he saw the constuction. Kirk was not the first Captain of the Enterprise. Remember how backward the episodes that featured Captain Pike looks, almost like 10 years before or more.
I look at the constructuon yard as a simple place to construct ships. Remember that there was a fleet out there beyond the Enterprise. Look at the primary epiodes, there are many many more ships! So the Enterprise was noe the only one being constructed. It was only one of a fleet of ships.