As far as we are aware neither developed any kind of open sea navigational technology like what is featured in Sunset Invasion, with sails being a particular piece of sea faring technology that was, at the very least seemingly not very common, but that is not to say that sea faring technology didn't develop, there is a body of evidence for sustained maritime commerce between South America, the Caribean and Mesoamerica for a very long time given the exchange of products like maize from Mesoamerica to the Andes, the expansion of metallurgic techniques from Ecuador to Mexico and the presence of of Mayan and Aztec products all throughout the Caribean and there is at least some evidence of maritime commerce in the area surrounding the Gulf of Mexico towards what is the modern Southern US as well as a host of cultural and religious points like in Mesoamerica Tlaloc and his counterpart Chalchitlicue being gods associated with both commerce, travel, and bodies of water.

This very thorough post about maritime culture in the Caribean in particular might be of interest to you.

Additionally u/400-Rabbits made a very detailed summary of what we know about maritime trade over here and I do recommend you check it out in its entirety as it is very informative though if you need a tl;dr I think this paragraphs will answer your direct question:

Could any of these vessels have traversed the Atlantic over to Afro-Eurasia? Sure, anything is possible, though not everything is likely. Mesoamerican/Caribbean dugout canoes, even with the raised prows and sideboards intermittently attested to in sources would have a very difficult time. Their design was shaped by their use in a landscape that permitted island hopping. South American balsas might have faired better, had they been ported across Central America and launched in the Caribbean...

The South Equatorial Current sweeping westward from Southern Africa to Northern Brazil and the Northern Equatorial Current flowing out from Northern Africa to the Caribbean are the best analogs to the way the Gulf Stream sweeps north and east towards Europe. Montenegro et al. (2006) are actual academics who modeled drift and paddle trips from Afro-Eurasia both under present day conditions and at the Last Glacial Maximum to investigate the chance of incidental crossings in the past. They found that, even with paddling, the journeys they modeled looking at trips along the above currents took an average of 90 days and less than 80% of simulations even resulted in a complete crossing.

Coastal civilizations of coastal Peru had the ability to sail the Pacific ocean and reach new lands, there are some foundational legends of great heroes arriving from distant lands in large fleets to create new settlement. (Legend of Naylamp). Also their shipbuilding technology survived into the colonial times and still used effectively alongside European vessels untill they where simply outclassed and only small precolonial fisherman boats are made nowaday

The Inca later conquered the coastal civilizations and took over their naval expertise and technology for themselves. During the reign of Inca Pachacutec, his son and later emperor Tupac Yupanqui created a great fleet and sailed to what's now suspected to be Polinesia where entered in contact with the local populations. The Spanish chronicler wrote this information down from the Incas, and later investigations like the ones made by historian Jose Antonio del Busto or Kontiki showed that the prehispanic ships where able to leave the coast and arrive in Polinesia. Interestingly, some Polinesian islands are said to have legends mentioning some king Tupac that came from the east and bring new thechnologies with him

Other sailing civilization was the Chincha kingdom that where great merchants that sailed the coast, even arriving to central America