In the year 500 AD the Empires of Europe and Asia where having there fun. Then an empire sent a ship off to finally prove the world was flat but boy did it end badly.

Use empires from around 500 Ad to 1000 Ad. Use 500 Ad technology. No columbus this is alt history. If you want more ask

Can I play the Byzantines?

also, you know that people knew that the world was round during the middle ages, right? They had known since early Antiquity, the whole "medieval people thought the world was flat" myth came from a 19th century pseudo-biography on Christopher Columbus, and was later perpetuated by the Anti-Church movements to try and claim that they were making people ignorant and backwards. The idea that educated medieval people, the ones who would be commissioning a voyage, believed the earth was flat didn't appear until the 1930s. If anything, the opposition to Columbus in OTL was because they thought his math was wrong and he miscalculated the distance his ship was capable of traveling.

(Shhhhh, don't tell them that, they aren't supposed to know)

Yes I know. I just used it as I could not think of any other reason for them to explore. And yes Byzantium is epic. You may use them