How about a TL in which the European Christians win control over the Arab region, retaining full access to the Silk Road, and thereby negating the driving impetus behind naval trade between Europe and the Orient?
This impetus could also be denied if, instead, the Mongols conquered the entire Europe, devastated it as they did in Persian regions, and spreaded their influence as they did in China. Europeans would have an entire continent to explore, and wherever they went they would be received as part of the Mongol community and, maybe, as Muslims. Still, maybe they reached America by chance, especially when they were sailing around Africa (ships are better freight vessels than camel caravans) and reached Brazil by chance. The OP is about reaching the continent, so it would be done, but it's unlikely that they would show any interest in colonizing the region any soon.