Well let's do the math.
Kirk was born on the Kelvin medical shuttle (#37) in 2233.
The main events of the movie take place in 2258 with the arrival of Ambassador Spock from the singularity.
2258 - 2233 = 25 years.
Thus, Kirk is 25 years old when he gets suspended, promoted to first officer, jettisoned off the ship, meets Spock Prime, pisses off young Spock, takes command, and relieves Pike as commanding officer of the Enterprise.
Kirk was born on the Kelvin medical shuttle (#37) in 2233.
The main events of the movie take place in 2258 with the arrival of Ambassador Spock from the singularity.
2258 - 2233 = 25 years.
Thus, Kirk is 25 years old when he gets suspended, promoted to first officer, jettisoned off the ship, meets Spock Prime, pisses off young Spock, takes command, and relieves Pike as commanding officer of the Enterprise.