Obviously there was nobody qualified to translate, so I'm guessing the entire continent was just miming to one another for a few years until people started learning the European languages? Would the Europeans learn the native languages? Did the Conquistadors ever know that the Aztecs thought they were gods? Did Columbus have a couple translators on board for when he reached Asia?
So many questions! I think that's enough.
There's always room for discussion, but perhaps the section Cross-cultural communication and lingua francas from our FAQ will answer your inquiry.