Portuguese fishermen had been fishing the grand Banks by the time of Columbus and it is quite likely that they made landfall. In any event there are accounts of bodies of Eskimos or Inuit Indians being observed by these fishermen.
It appears that the ancient world was remarkably advanced. One wonders what might have happened if Islam had not helped precipitate the dark age?
Columbus gathered information in Iceland regarding the western lands, which were known about by Icelanders and other Scandinavians (and obviously the rumors had made their way around Europe). There are a couple of known Viking sites in Canada (plus some others in northern N.America which are not necessarily generally accepted) and the surviving saga material.
Iceland was also settled prior to Viking settlements, probably by Irish monks, although it sounds like they'd given up and left, or merely died out.
And thousands of years ago the Maritime Archaic ("Lost Red Paint People") appear to have settled all 'round the Arctic coastlines, leaving similar stone markers which appear to have indicated safe places for landfall. One researcher has apparently suggested that the Red Paints didn't erect the stones, but figured out their significance, and that the markers are much older, placed by an earlier circumpolar culture.
The Maritime Archaic, Palaeoeskimo, and Na-Dene speakers (although the Inuit/Eskimo groups isn't genetically related to the Beothuk in eastern Canada) arrived in succession, each having a period of dominance, but culturally distinct from one another, and each supplanting the previous group, with possible survivals in pockets here and there.
Naturally, any model that indicates that humans who live by spearing various aquatic life are good enough with boats that they can cross a fairly narrow strait causes high blood pressure, incoherent rants, and other symptoms among the landlubbers who will defend Clovis-first-and-only until everyone with any sense is tossing a symbolic handful of soil onto their interments.