Early Irish writings, including the ‘Imramma’ poems, identify Irish monks sailing to North America. Later writings, including the Brendan Voyage do likewise.
The Norse annals, which were intended as historical records, do likewise, in the Landnámabók and the Annals of Greenland, which itself is written evidence supporting the now-accepted fact that the Vikings had reached North America in the 11th century.
Throughout these texts, this land is referred to as Írland hit mikla (Greater Ireland) or Hvítramannaland (White Man Land) due to the perception of those who were resident there.
Even in 12th century Sicily, the Arab historian Al-Idrisi wrote of the existence of Irlandah-al-Kabirah, or Greater Ireland, located to the west of Iceland.
And the Shawnee legends of the Amerindian peoples near Chesapeake Bay refer to the existence in their history of white men carrying poles and using iron instruments.
And artifacts have been found in locations including West Virginia which bear marks cognate with the Ogham script of ancient Ireland, though this is disputed.
This is all generally hand-waved away by contemporary historians as mere mythology, as they quite reasonably insist on incontrovertible archeological evidence.
Mind you, they used to do the same thing in relation to the Vikings until Anse-aux-Meadows was discovered. Even then, they still attempted to argue away the Helluland site on Baffin Island, even sacking the archeologist and her husband and sequestering her evidence.
I’m always intrigued by such historical disputation, and often wonder cui bono? Could a narrative which supported earlier European engagement with North America in anyway undermine Canadian claims to the wealth in and under the Arctic, for example? Such has been alleged in the past.
In any case, I hope they do find Greater Ireland one day, just as they appear to have already found Vinland and Helluland.