It is true that it's set in a time (stardate / year-wise) before Kirk and Spock et al had their 5 year missions etc.
However it's also a "re-imagining" (see 'Planet of the Apes', 'Battlestar Galactica', 'Batman Begins'
etc) so it does not have to comply with anything that we already have seen on TV or in films.
If it were a prequel, then we would know what was going to be in their futures.
In this film, the Enterprise might get destroyed, or Kirk and Spock might get killed (it's never gonna happen, but it
could because it's a reboot).