2255

Multiple realities
(covers information from several alternate timelines)

Events

The Sheliak attempt to communicate with the Federation, something they will not do again until 2366. (TNG: "The Ensigns of Command")
Ensign James T. Kirk, on his first planetary survey mission, visits the planet Neural, where he meets Tyree. (TOS: "A Private Little War")

According to the Star Trek Chronology, James T. Kirk would have been stationed on the USS Farragut during his mission to Tyree's planet.

Alternate reality

The USS Enterprise undergoes construction at the Riverside Shipyard in Iowa. Several Starfleet Academy cadets, including Nyota Uhura and Hendorff, spend some time in Riverside. (Star Trek)
James T. Kirk gets in a bar fight with Hendorff and three other cadets at the Shipyard Bar in Riverside. The fight is broken off by Captain Christopher Pike, who later talks to Kirk about joining Starfleet by reciting the incident resulting in the destruction of the USS Kelvin and his father, daring him to do better. The next day, Kirk boards the military shuttle Bardeen, enlisting in Starfleet. (Star Trek)
Leonard McCoy gets divorced from his wife and enlists in Starfleet, boarding the same transport as Kirk, resulting in a friendship between the two. (Star Trek)

Mirror universe

The Terran Empire's new flagship, the ISS Charon, is launched from the Imperial Shipyard at Epsilon Indi IV. (DIS: "Terra Firma, Part 1")
Gabriel Lorca and Michael Burnham begin their attempted coup d'état against Emperor Philippa Georgiou. (DIS: "Terra Firma, Part 1")

No date is given for these events, but given that Lorca's co-conspirators spent almost two years in agony booths after the failed coup (as seen in "What's Past Is Prologue", set in late 2256 or early 2257), the coup presumably began in mid-2255.