I've always conjectured that Pike was born around 2215 which would have made him roughly Kirk's age when he first assumed command of the Enterprise from Robert April. Commodore Mendez did say that he was roughly Kirk's age but that could have been a reference to Pike's age at the time he served with Spock aboard the Enterprise.
We know Georgiou was born in 2202 based on the Shenzhou library computer records that Voq was looking at after the Klingons boarded the ship. That would make her perhaps a decade older than Pike but not necessarily preclude the two attending the Academy at the same time.
We know Georgiou was born in 2202 based on the Shenzhou library computer records that Voq was looking at after the Klingons boarded the ship. That would make her perhaps a decade older than Pike but not necessarily preclude the two attending the Academy at the same time.