We know TOS season 1 was 15 years before ("Space Seed" - WoK), and "The Cage" 13 years before that. So the Enterprise should be a minimum of 28 years old at the time. But if you include the animated series, there was April before Pike.
The Encyclopedia puts the Enterprise launch in 2245, but that assumes 5-year missions, which Into Darkness established (for the Kelvin universe, at least) that the first five year mission launched was under Kirk.
The Encyclopedia puts the Enterprise launch in 2245, but that assumes 5-year missions, which Into Darkness established (for the Kelvin universe, at least) that the first five year mission launched was under Kirk.