Talking about a non-colonial Western hemisphere causes some difficulties of nomenclature. Many of the now-common names for peoples and nations are not the names those people would have used, and almost certainly not the name that would have been used had those people continued to flourish. In order that the greatest possible number of readers understand, though, I have used what seem to be the most common names while attempting to also use the local name as often as possible. I hope the result is both understandable and inoffensive!
Note: This should by no means be taken as a comprehensive timeline. It is, rather, an outline intended to hit the key points of technological development and historical alteration. All named individuals are actual historical figures.
5th C or so: A Phoenician ship, blown greatly off course, lands within the Mayan sphere of influence and is unable to return home. Their phonetic alphabet influences Mayan writing more toward phonetic characters, though there are still ideographs mixed in. The tale of the Phoenicians’ trade empire plants the seeds of ideas for extensive trade by sea that will flourish centuries later.
8th C or so: Tang China makes some very speculative trade overtures along the island chains of Oceania, and by this means smallpox is introduced to the Western hemisphere. It causes considerable devastation in the first generation before reaching equilibrium and establishing itself as endemic.
10th C: The Maya have writing, mathematics, astronomy, medicine, ceramics, metalworking, and the seeds of a merchant class thanks to their trade network. Public architecture has reached a peak, but it is a peak of decadence and resentment is starting to stir in the peasant class over the heavy draft-labor tax that only seems to put more flourishes on existing construction. The Maya depend on rainwater for their potable water source, and while this has spurred considerable hydro-engineering accomplishments, it is a vulnerability. When long drought leads to famine, unrest, disease, and the collapse of southern trade routes, the southern cities are abandoned. The refugees bring civil unrest to the cities of the north. The noble class is unable to control the unrest, and Chichen Itza, now the premier city of the nation, undergoes a full social revolution. This spreads to their ally Uxmal and beyond to the other cities. The resulting overthrow and recreation of the ruling class establishes greater rights for the peasants, especially lower draft-labor taxes and increased property ownership. Writing, always a mark of the nobility, is gradually taken up by the merchant and artisan class. Both developments re-invigorate the culture and open the way for some innovation. The reduced population encourages labor-conserving devices, from simple winching through pulleys and wheeled carts. All this, and especially the social restructuring, may have gotten a boost by isolated explorers from the Abbasid Caliphate.
11th-12th C: Metalwork advances, and the military nobles push ornamentation more and more toward armor and weapons. Population begins to expand again, and return to the southern cities and a bit beyond the old borders. The experience of the drought spurs the development of techniques to access underground rivers. Communications are a priority during expansion, leading to signal towers as well as couriers. Levering technology is applied to ceramics production, leading to a variety of potting wheel, and press-forms that produce tiles for building; this is the seed of mass production. Advances in kiln technology lead to the use of coal and oil.
Maya: Mayapan does not become premier city; Chichen Itza’s sea port is too important to trade. In 1441, Ah Xupan Xiu of Uxmal’s revolt against Mayapan domination and their supporting mercenaries does not happen. There are, however, new cities founded on the west coast to create new trade access there.
Inca: The Incan Empire rises, and trade relations are established with the Maya by sea. Imports include writing, adapted in a more syllabary form to the Quechua language, and improved metalwork; medical science is shared; the middle class is strengthened. True science and technology specialists develop among the artisans of both empires.
Aztec: The Aztec Triple Alliance rises among the Nahua city states. The Alliance has trade with the Maya (and the Maya have the few remaining copies of Aztec written history that Tlacaelel re-wrote). The Alliance also has trade contact with the Cherokee, and through them the Anasazi/Pueblo and the Iroquois and the Northern trade network in general.
Maya: The Maya, wanting more direct contact, through less dangerous intermediaries, with their northern trade partners develops their sea-going trade and contact the Anasazi/Pueblo nation. The Anasazi/Pueblo develop as a trade nexus between the western Anishinabek and the Maya. Expansionism of the Aztec Alliance spurs the Maya to increase development of military weapons and tactics, including catapults and crossbows, eventually leading to spring-powered, barrel-guided arrow guns.
Northern nations: Maritime expertise is passed down the trade routs from the Athabascans and Inuit, worked goods are traded up for raw materials, cotton for fur; metal weapons are much prized all over north. Information is passed along with trade, especially as Mayan and Incan writing spread and are adapted. The Iroquois Five Nations rise to prominence in the east, and are a major influence for gender equality. Law and history begin to be written down in all the stable nation/tribes, and coastal sea-faring grows.
Maya: The Spanish arrive, and Uxmal does not ally with them to throw down Mayapan. There is a brisk demand for weapons and construction techniques to the north, and the discovery of gunpowder results in significant advances in this area. Mayan wealth and security grow.
Aztec: The Tlaxcalteca, a long rival of the Mexica, do ally with the Spanish to break the Aztec Alliance, but the power of the Maya to the south and Anasazi/Pueblo to the north discourage further expansion and the Mexico valley becomes a mixed Nahuatl-Spanish nation and government.
Inca: Huascar Capac, prince of the Inca, dies of bad fish before his father, leaving his militarily savvier half brother Atahualpa (child of a royal northern treaty-bride, tying the north tighter to the south for his time) to take the throne and meet the Spanish with the full loyalty of the military behind him and better materials equality. This prevents outright conquest, but the Spanish do stir up a certain amount of unrest in the empire, despite Atahualpa being the child of a royal northern treaty-bride and thus having greater support in the northern empire than his brothers. The unrest does not have quite the effect the Spanish hope for, however; the Empire may eventually break up into smaller pieces, but this leaves no overarching social control mechanisms, such as draft-labor, for the Spanish to take over. Cultural continuity and political integrity are largely maintained.
Northern nations: Britain and France’s trade relations with the Iroquois and Algonquin go much as they do in our timeline, except that the Iroquois and Algonquin, having heard about the attempted Spanish invasions and the Aztec defeat, refuse to allow wide-spread settlement or to sell land. They refuse very firmly, to the point of sinking ships that attempt to land outside the established trade ports and attacking settlements outside the trade cities inland. There is still a good deal of taking up allies’ wars among the various native and immigrant nations, however.
Southern nations: Without the leverage for conquest, the Spanish missions turn to trade and exploration in search of natural resources. This results in a fair number of local conflicts, but does not threaten the stability of most established nations. The stable nations become valuable trade partners, and the influx of arts and science techniques from the other hemisphere touch off a new wave of innovation and development.
Americas: Conflicts all over both continents lead to a rush to assimilate each other’s technology, producing a patchwork of nation-states with very cosmopolitan and hybridized cultures and sciences. Trade and war are both brisk, all over the globe. There is little demand for the Atlantic slave trade, which doesn’t really get off the ground.