I dont think "ancient civilizations" is a fair description. Some of them only, and few compared to the number of civilizations. And even in the ones where it was known, that knowledge was most probably only shared within a small group of scholars.
The page documents how this then filtered into Roman and early Muslim astronomical traditions. Granted, since only a small percentage of people in these societies were literate, it was probably true that most people in, say, the Roman or Sasanian empires thought the earth was flat. But given what we know about the ways that premodern books were read (often in public, sometimes to a large groups of people) it seems to me like an open question.
There's also this very interesting aside about the possibility that the Phoenicians also knew the earth was round, perhaps even predating the Greeks: "In The Histories, written 431–425 BC, Herodotus cast doubt on a report of the Sun observed shining from the north. He stated that the phenomenon was observed during a circumnavigation of Africa undertaken by Phoenician explorers employed by Egyptian pharaoh Necho II c. 610–595 BC (The Histories, 4.42) who claimed to have had the Sun on their right when circumnavigating in a clockwise direction. To modern historians, these details confirm the truth of the Phoenicians' report and even open the possibility that the Phoenicians knew about the spherical model. However, nothing certain about their knowledge of geography and navigation has survived."
Even before Christ, they used to just hold globes. It's the same image as that "evil megacorporation controlling the world" hand-holding-Earth image we've all seen before.
My point is that they seem to have known continuously since ancient times that the Earth was a sphere. They were using globus crucigers the whole time. Even in the Dark Ages, the Byzantine Emperor had coins made with his image holding such a globe, around 700AD.
It seems more like they'd know the Earth was round but really have no reason to care or spend any time thinking about it, the same way we don't spend time talking about the microwave background radiation from the big bang or the structure of our local galactic supercluster. These people didn't even have a standard unit to measure bags of grain from one village to the next. Assuming they had any grain to measure at all.
https://en.wikipedia.org/wiki/Globus_cruciger
(Incidentally the ritual orb which Elsa must take in Frozen is a politically correct de-Christianized version of this).
Don't forget that the literacy rate for pre-modern societies was 10% and probably much lower on average. There were some extreme exceptions, I think the Hebrews had much higher rates, but as a whole, the world's population couldn't even write their own name.
As for illiteracy - it's not always necessary to be literate in order to know something. In our modern world there's a great many things 'everybody' knows, without necessarily ever having read about it. True things as well as false things, obviously.