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.
2245 is more of a conjectural date. The TOS Constitution class starships look like they were built in the mid 22th century.