Columbus was trying to reach Asia but thought the Earth was smaller than it is so he travelled west hoping to reach Asia with the enough supplies he had. Luckily (for him only, of course) the amount of supplies he had was just the amount of resources he needed to reach America. However he thought that he was in Asia (that's why he called the Natives 'Indians' because that's what Europeans used to call Asians). So when did the colonialists know that they were in America not Asia?
This question has been asked a number of times before, and I gave one answer some half a year ago. I hope it is useful.
https://reddit.com/r/AskHistorians/comments/ebrc7c/how_did_europeans_figure_out_that_the_lands/