Hatching was the act of breaking an egg from the inside in order to exit it. One who had just hatched was called a hatchling, while a location where hatching took place was called a hatchery.
Every 11 years, the giant eel-birds of Regulus V returned to the caverns where they were hatched to mate again. (TOS: "Amok Time")
In 2257, when challenged to another round of the autoantonym game by Jett Reno, Linus replied he was "hatched ready". (DIS: "Through the Valley of Shadows")
Linus's statement suggests Saurians laid eggs to reproduce.
In 2267, Spock noted that the Horta eggs were about to hatch. Later Chief Vanderberg informed James T. Kirk that they had begun to do so. (TOS: "The Devil in the Dark")
In 2364, noting the android's unusually pale skin pigmentation Felix Leech asked Data where he was hatched (i.e. born). (TNG: "The Big Goodbye")
In 2372, a Reptohumanoid young hatched, which Tom Paris noted when calling USS Voyager. (VOY: "Parturition")