One of my favourite books from years ago is The Ra Expeditions by Thor Heyerdahl. He built a boat out of reeds, following ancient Egyptian models (not even wood!!) and sailed from Morocco to Barbados. He also built the Tigris, another reed boat, and sailed from the Persian Gulf to Djibouti. Although I am as quick as any to point out the limits of experimental archaeology, reconstruction, and re-enactment, Thor certainly did demonstrate that very old boats were absolutely capable of long voyages. And Tim Severin is almost an Irish national hero for The Brendan Voyages, in which he actually sailed a leather (still not wood!!) currach to Newfoundland.

So yes, it could have been done. Not the same as it was done.