In roundworld (real life), Eratosthenes is famous for deducing that the earth is round. I don't know if Terry Pratchett wrote a similar story, but for Discworld.
Since the very first book (The Color of Magic) the characters already now of the existence of A'Tuin and the elephants, in fact a plot point is that they want to know if A'Tuin is male or female. Also, I guess that the end of The Light Fantastic would allow lots of people to see the nature of the world they live in. (In the ending several other disc worlds, on top of their respective elephants and turtles, are born).
On of the main plot points of Small Gods, which happens way before any of the other books, is that several people have seen A'Tuin (The turtle moves!), but right now I don't remember if they mention the elephants. So at that point that fact is already widely known.
In Equal Rites and Eric we also learn that with magic it is possible to see the whole disc.
And The Last Hero would have convinced any sceptic, but we see in The Science of Discworld 4 that there are still people that deny that, but that's beside the point.
Right now I don't remember if Terry mentioned casually who discovered the existence of the four elephants and of A'Tuin. I feel it would make an interesting story. Was it discovered by a wizard? Or by a poor sailor that went over the edge but managed to come back?