The textbooks you refer to are generally old and were written with a Euro-centric orientation. Meaning, the first European who made a well-documented visit to this continent and came back and spread the word, was St Brendan, in the 8th Century AD. However his voyage is expressed in partly mystical terms, so a limited case remains for continuing to acknowledge Christopher Columbus.
If you look at more modern textbooks, they generally acknowledge that the American Indians were here first, and that they were other explorers before Columbus, most notably the Vikings about 500 years prior. An 11th-Century Viking presence at L'Anse aux Meadows in Canada has been demonstrated archeologically in recent decadees, and is reasonably consistent with the Viking Vinlandinska Saga, whose origins lie in the Viking outpost in Greenland.
In simple chronological terms the first widely acknowledged claim for a voyage from Europe to North America is that attached to Prince Madog ap Gruffydd of Gwynedd Wales, but this is hard to substantiate as he did not return, and the claim is largely based on the authenticated doscovery of a Welsh-speaking tribe in North America in the 1640s.