2223 — memory alpha

Events

Relations between the United Federation of Planets and the Klingon Empire degenerate, giving rise to some seventy years of unremitting hostility as the two powers become embroiled in a tense cold war. (ENT: "In A Mirror, Darkly, Part II")
December 29 – Joseph M'Benga is born in Kenya on Earth. (SNW: "Under the Cloak of War")

According to the script notes for the Star Trek: The Original Series episode "Operation -- Annihilate!", Sam Kirk was "older by ten years than the Captain", implying this as his birth year.
This year, seen in a timeline on a computer screen, was apparently derived by subtracting seventy years from 2293, the year Star Trek VI: The Undiscovered Country is set in. That movie contained a line of dialogue where the Federation and the Empire were said to have seen almost (rather than exactly as the timeline would suggest) seventy years of "unremitting hostility", the same phrase used in the timeline.
According to Star Trek: Star Charts (p. 33), after becoming warp-capable, Delta IV is admitted to the Federation.