This may not be the first generation starship tale, but it's probably the first where the passengers have forgotten that they're in a ship and that its corridors and rooms are not the universe.
This novel combines the story of Galileo with political intrigue and military conquest, all aboard a starship that has lapsed into feudalism after a mutiny in the crew long ago. After the mutiny, people forgot not only their mission to travel to Far Centaurus but that there was a universe outside the ship's hull. Books are still around, but physics and astronomy are treated like elaborate allegories by the "scientists" and not realities. Barbaric muties roam the upper decks, and cannibalism is not unknown, infantcide a common practice.
Scientist novitiate Hugh Hoyland plays the Galileo role. He is captured by two-headed mutant Joe-Jim and, when he's not playing checkers with either of the twins, has the run of their library and the benefit of their intellects. It's from that unlikely source that Hoyland learns the truth about the ship and the world outside.
And he begins to form a plan to complete the mission.
First published in 1941 as two short stories, "Universe" and "Common Sense", this story still entertains with its heroism, intrigue, and action. They are, chronologically, also the last short stories in Heinlein's Future History.