Doing so requires either knowing where to catch the right wind, which is how Columbus did it, or having galleys of rowers, who would need to be fed, which would require a large hold for provisions. Not doable, especially since nobody knew the land existed where it did in order to plan for it. Ptolemy believed the world was a perfect sphere, so anything on the other side of the globe, by his calculations, would be much closer than it actually was, which is why Columbus thought he was in India when he was only in a Caribbean island chain.