They have other evidence of Polynesian contact, various earlier European contact, Vikings, perhaps Japanese fishermen, Oceanic people related to the Australians, the occasional African and accounts of Chinese contact. It seems that people have been bumping into the Americas for some time. Columbus just gets the credit.
The basic idea is that lots of folks got to the Americas one way or the other but almost no one made the trip back home, or none who made the trip bothered to tell anyone about it, or a variety of other reasons.
There are some very good reasons why this is so ~ sea currents are the big one, PLUS, the problem of icebergs in the North Atlantic combined with the incidence of Hurricanes in the Caribbean and along the Gulf Stream, leave only a very narrow window of opportunity to return.
Columbus figured out when to go and when to come back ~ and told folks about it. So he gets all the credit.