Alternative History

1500: On their third expedition to Atlantis, the Castillians discover Cuba. This marks the beginning of the colonization of the Caribbean. On their return, they also discover the Bahamas.

A ship from Braunschweig-Lüneburg discovers Bermuda by accident.

1500-10: Settlement of Cuba by Castillians.

1502: Motehcuhzoma II becomes ruler of the Tenochca.

1504: Jamaica discovered by Castillians.

1507: Castillians found Veracruz at the site of OTL New Orleans, start exploring the Mississippi valley.

1509-12: After some clashes with Danish colonists in Atlantis, the Quadruple Monarchy starts anti-Danish War against, surprise, Denmark. Dutch ally with them. In the peace of Hamburg, Denmark loses its lands in Canada to the Quadruple Monarchy and Anderland to the Netherlands. Only the city of Haraldsborg (OTL New York, plus Long Island) and Prince-Haralds-Land (Newfoundland, as a base for fishermen) stay in their hands.

1514: French send an expedition to the Caribbean, claim OTL Hispaniola for themselves, which they call Nouvelle France.

1517: Puerto Rico becomes Castillian colony.

1518/19: Castillians subjugate the first Maya cities. (There are/were a lot of political entities around, each of had to be defeated independently, other than the Aztecs or Inca.)

1520: A small Castillian expedition (a few dozen men) meets the Tenochca. They're defeated, noone returns. However, the Castillians beat the Tenochca at Tapachula (south of OTL Mexico).

1521: The only surviving heir of the Norwegian (and Scottish) throne, Prince Alasdair / Alexander goes to Atlantis, where he spends some time around the Caribbean. He also approaches the Tenochca and learns about their gold riches.

1522: Prince Alasdair comes to the court of France, warns the king that the Quadruple monarchy is about to conquer the rich lands of the Tenochca. He points out: "If the king owns their gold, he can afford to hire all the mercenaries in the world! You have to stop him now!"

1523: Castillians want to send an expedition to Tenochtitlan, but the ship from Cuba is destroyed in a hurricane, and until replacements are found, necessary time passes.

1524: France manages to smuggle some hundred soldiers and advisors to Atlantis to help Cuitláuac, the military leader of the Mexica, as the Tenochca are now called in Europe. The Tenochca have to convert to Christianity, however.

1526: Battle of Cempoala. French-Tenochca defeat Castillians.

1527: Huayna Capac doesn't die.

1527: Motehcuhzoma II dies, Cuitláuac becomes new ruler of Mexico.

1528: King Henrik VI of Scandinavia takes advantage of the war, takes the islands of Virgin Islands, Anguilla, Saint Christopher and Nevis, Antigua and Barbuda, and Montserrat for his empire.

Huascar, son of Huayna Capac, caught conspiring against his brother, the heir of Huayna Capac, named Ninan Cuyochi.

1529: Smallpox hit the Mexica... however, the Allies of the Quadruple Monarchy aren't better off, so it's a two-sided damage.

Motehcuhzoma II dies too, Cuitláuac becomes new ruler of the Mexica.

1530: Castillians explore the north coast of OTL Columbia and Venezuela, discover the Orinoco mouth, occupy the Antilles, build first settlements in South Atlantis.

1531: Dutch found colonies on Guadeloupe, Dominica.

1532: Huayna Capac dies.

1533: Braunschweig-Lüneburg claims the islands of Martinique, Santa Lucia.

1535: Castillians drive the French-Tenochca back to the heart of the old Tenochca Empire, ally with their old enemy Tlaxcala. Only the lack of support prevents them from winning completely.

1536: Florentines take Saint Vincent, Grenada, Barbados (which they call Elba Nuova).

1538: Castillians cross the isthmus of Panama, discover the Pacific. They learn about the lands of the Inca.

1539: Poland joins colonial powers, takes Trinidad and Tobago.

1541-50: Inca conquer Chibcha lands in OTL northern Columbia.

1543: With Scandinavia in Civil War / unrest, the other powers use the opportunity. Nystad, the capital of New Sweden, is taken by the Dutch; the South and West of the Chesapeake peninsula goes to Italia Nuova. The Netherlands and Florence make a treaty, ruling the border between their colonies in Atlantis, and promising to respect their borders.

1544: In Haraldsborg, the (almost) last Danish colony, chaos ensued after the mother country fell into civil war. Poland sends soldiers to the city, occupying it. Haraldsborg becomes the portal for Polish and Prussian immigrants to (Northern) Atlantis.

1545: Battle of Ile de la Tortue (OTL Tortuga). French defeat English-Castillian fleet.

1547: After the end of the Great Occidental War, Europeans start regular trade with Mexica and Tawantinsuyu (Inca empire). They keep their independence because neither power wants the other one to own their rich lands. The Quadruple Monarchy cedes West Florida, Panama and the Mississippi valley to France, western Anderland to France's ally Denmark.

1548: French governor starts work in Veracruz, which is renamed Nouvelle-Orléans. France and Scotland found each a harbor city in Mexico to trade with the Tenochca, and another two at the foot of the Andes, to trade with the Inca empire too.

1549: French monks arrive in the Inca Empire to convert the population to Christianity.

Chaos TL in blocks
Earlier in time:

Western Europe / Atlantis 1450-1500

Atlantis

1500-1550

Later in time:

Atlantis 1550-1600