There were several Nordic expeditions into North America before Columbus and they documented these expeditions.
I assume the existence of the Americas was more well known in the north and among the wealthy. I would also imagine that the knowledge the voyages would be pretty obscure in everywhere except Iceland and the people that did know about it either didn't have the resources act on the information or was indifferent to the existence of another continent. I'm pretty sure that most people that knew about the saga would not think of it has a myth, since that was how historical records were kept. But I could be wrong.
There also were a lot of migrations between Asia(including Polynesia) and the Americas but I don't think there was any contact for thousands of years before Columbus.
How common was the knowledge that the Americas existed in the old world before Columbus?
/u/Sagathain has previously answered:
/u/Reedstilt has previously answered Do any Native American/First Nations peoples have any oral traditions or tales about the Vikings?
Someone else might have more to say on the topic.