Cruisers numbering hundreds if not thousands per yer make the trek across the Atlantic without much fanfare. I've read stories of sailors on 26' ketches making it from Cape Verde to the eastern Caribbean. Most cruisers over 38' are comfortable enough to provision and cross in less than a couple weeks, depending on winds.
The difference between then and now is that we know the boundaries of the Atlantic thanks to cartography and satellites. Back then, to them, it was just open ocean as far as the imagination could go. As long as they stayed out of the doldrums and sailed right west, they could conceivably make it on personal watercraft. Would take some serious stones to want to do that though.
The guy that taught me how to really sail was making his second lap around the world in a 28 foot Beneteau.
The Polynesians did it in the Pacific. Just because we don't know how they would have done it doesn't mean that they couldn't have figured it out (it also doesn't mean that anybody did figure it out).
It is only very recently that the navigational technology of the Vikings has been re-discovered.