I think it is possible that Phoenicians, Romans, and Greeks made it to the New World. Probably would have been a one way trip tho.
There’s no reason it would have to have been a one way trip.
The Lowly Amphora (and ancient contact across the oceans)
http://www.freerepublic.com/focus/chat/3295687/posts
The Roman Head From Tecaxic-Calixtlahuaca, Mexico: A Review Of The Evidence
http://www.freerepublic.com/focus/news/1304316/posts
Romans in Brazil During the Second or Third Century?
http://www.freerepublic.com/focus/bloggers/1248340/posts
Ancient Romans In Texas?
http://www.freerepublic.com/focus/news/665767/posts