There is a roman ship that was once found of he coast of Brazil, which caused a huge stir. I think they later traced to a deliberate plant by a named person
But it was a huge thing. Then there is the story in the west African chronicles about Abu Bakr II who allegedly crossed the Atlantic and was never seen again. And there are also stories of Romans both in Nigeria and in China. These latter theories are more founded in fact. But you could make entertaining novels on such speculations. There has also been a book about China discovering the Americas, and Thor Heyerdal's speculation about about the crossings of oceans of rafts in the 1940 and 50s.
There is also the great mystery of Göbekli Tepe in Turkey, an extremely old temple whose construction presupposes organized learning and division of labor. The reason why it remains a mystery is because the Ice Age wiped out all the archeological evidence that would place the construction in context.