There was an article a couple days ago about why everyone believes Columbus proved the world was round[1], even though that isn't true[2]:
The real myth of the medieval flat earth begins first
in the eighteenth and nineteenth centuries and has
two principal sources. Probably the most influential
of these was the American author Washington Irving
who in his fictional biography of Columbus claimed
that Columbus had to fight against the Church’s
belief that the world was flat in order to get
permission and backing for his voyage, a complete
fabrication.
I see an interesting parallel between the two cases. When you're the most influential person talking about something (or the only person at all...), people who later want to learn about the subject treat you as the best available authority, even if you're a bad one. Information is copied from authorities and self-reinforcing over time, much like genes in a population. What that means is when there's a bottleneck in the number of people talking about a topic, you can see a founder effect[3].
Of the many sources to demonstrate that it was well known that the Earth was round, I like Dante the best: His Divine Comedy explicitly described the world as spherical, described how that meant different parts had day and night at different times, described how the stars would be different, etc.. It's not a very early source - there are many earlier ones -, but his level of detail shows that it was well understood what it meant and that the idea could be published in a work dealing with religion without controversy in the middle of Europe.
[1]https://thonyc.wordpress.com/2016/05/25/repeat-after-me-they...
[2]That Columbus proved it, that is, not that the world is round.
[3]https://en.wikipedia.org/wiki/Founder_effect