Columbus's third voyage, in 1498, took him past the Orinoco River delta on the north coast of South America. He immediately realized that the vast quantity of water meant this river had a substantial drainage basin, such as could only come from a continent. And, since he was on the north coast of that continent, this had to be a new continent.

So, this was the first time Columbus realized he'd found a new continent. He still didn't adjust his estimates of the earth's size, though - he thought this new continent was a short ways to the south of Asia.