There wasn't really any incentive for them to do so. The construction of large ships capable of travelling on the open ocean is very costly in terms of resources and human labour. The only societies in the Americas which were complex enough to bring these resources together weren't located close to viable sea trade routes. Plausibly some of the societies in the Caribbean and the adjacent mainland were complex enough that they could have developed large ship-building technologies given sufficient time, but at the time of European contact, many of these societies were experience a reduction in complexity due to changing climate, so their historical trajectory didn't seem to be in that direction. Even if they had developed such technologies, they would have had a lot of America to explore before anyone felt the need to see what lay over the horizon. In contrast, pre-modern Europe can reasonably be thought of a series of large bodies of water ringed by human polities, so the sea was much more important from a far earlier stage, and corresponding resources devoted to exploiting it. Asia is on the whole less easily conceived of in these terms, but contained vast enough populations that there were as many people as in Europe for whom it made sense to think of the world as a network of seas, and who correspondingly developed sophisticated nautical technologies. Even the Norse were still essentially island-hopping, which is a bit different than just sailing into the great blue yonder. The existence of other lands can be deduced from currents and birds long before they are ever seen, and it is very likely that this contributed to the Norse discoveries of Iceland, Greenland, and North America. Most of these discoveries will have been preceded by deep-sea fishing expeditions which obtained these "hints", rather than just somebody pointing into open sea. It's honestly a matter of dumb historical luck that the European discovery of America didn't more closely resemble this: Basque and Portugese fishing fleets had been visiting the Newfoundland cod banks for decades before Columbus landed on San Domingo, so it was probably just a matter of time before somebody figured out there was a continent just a few hundred miles West.