Mr. Laser Beam wrote:
Do we know for SURE that the original 1701 was built in 2245? IIRC, there's no canon reference to the year that it was constructed.
In any case, even if it was built in that year in the prime timeline, Starfleet may have decided to build it earlier in the Abramsverse. The same ship, built in 2233 rather than 2245. Or something like that.
The closest thing to canon we have is the Defiant's database in Enterprise's Mirror Universe story, though that portion wasn't actually visible on screen.
The only concrete reference to the Enterprise's age was in Trek III when Admiral Morrow says it's twenty years old, but that contradicts The Cage.