The Primeverse Enterprise
's launch date is not canonically established. All we know is that it was launched sometime prior to 2254 ("The Cage"). (There was a viewscreen graphic made for "In a Mirror, Darkly" that gave the Enterprise
a 2245 launch date, but it wasn't seen in the final episode.) Indeed, we can't even rule out the possibility that it could
have been launched before 2233.