In 1460, the ambitious duke Bernhard I of Braunschweig-Lüneburg, who inherited most lands of the Welfs, founded a colony in Atlantis at the site of OTL Philadelphia, called Martinsburg (with the help of the Hanseatic League cities Hamburg and Bremen).
During the Great Occidental War, when the major powers were distracted, Braunschweig-Lüneburg also claimed the islands of OTL Martinique, Santa Lucia in 1533.
In 1554, Braunschweig-Lüneburg formed its second province in Atlantis, called Waldstätten (OTL Pennsylvanian Appalachians). Experienced woodcutters and sawmill builders were invited there from as far as Switzerland.
Until then quite restricted in their possible development, 1628 king Kristian of Denmark died without heirs, and the nobles decided to make duke Ernst V of Braunschweig-Lüneburg new king. In 1642, the colonies of Denmark-Braunschweig (Martinsburg, Waldstätten, Nieuw-Nederland, Haraldsborg and Anderland) were united under a common administration. Around 1650, the settlements in the colonies of Denmark-Braunschweig and Florence, plus the New English Commonwealth, had reached the official border to the French-claimed territory, which was still mostly settled by native Atlanteans.
During the anti-French War, in the battle of Martinsburg, November 1689, the Danish fleet was destroyed by English and Italians. In the peace of Amsterdam, Denmark-Braunschweig received the northern part of Louisiane from France, if only to put a buffer between the settlements of England and Italy. Now they could expand again - 1700, Denmark-Braunschweig founded the ninth land, at the shores of Lake Erie. In the years 1706-14, they fought the War against the Five Nations. Historians agree that this war helped the mixed German-Danish-English-Dutch-Polish population very much to become a community. The war proved to be very hard, since the French left the Five Nations (actually seven nations meanwhile, the historical five ones and the Monacan and Connestoga in addition, being displaced earlier by European settlers) equipped with guns and boats. 1726, the Germans and Italians agreed to make the Ohio river the border between their possessions in Atlantis.
A generation after the last war, in 1746-50 they had to fight the French-Atlantean War (also called War of the Great Lakes). Denmark-Braunschweig and Britain fought the native Atlanteans and the French immigrants in Quebec (OTL Ontario). ~1750, the settlements of the Germans and Italians had reached the Mississippi river. In this very year, the city of Wildenhartburg was founded at the site of OTL Chicago.
In 1776, a canal connecting Ohio and Mississippi was built in German Atlantis. (South tip of Illinois was part of Italia Nuova.)
When Denmark-Braunschweig was defeated and subsequently dismembered in the Third French Republican War, in 1795 the "Schulzenaufstand" (Mayors' Uprising - yes, "Schulze" is an old German term for "Bürgermeister" / Mayor) happened in German Atlantis. They declared themselves independent, formed a confederation similar to Switzerland. Martinsburg became the new capital.
~1800, the German, British and Italian settlements had reached the Rocky Mountains, where they made contact to Novorussian settlers. The Germans founded Silberstadt in OTL Montana.
In the early 1800s, the two main political parties ("Die Freien" - "The Free Ones", and "Die Gleichen" - "The Equal Ones") emerged. They gave each other the nicknames "Die Nackten" ("the naked ones", implying they had no shame) and "Die Blinden" ("the blind ones", accusing them being blind for reality).
At the same time, the anti-slavery movement started to rise in German Atlantis, which would later spread to Canada and even later to Argentinien.
When the population grew, some leaders thought that the country needed new places for settlement. The opportunity came 1832 with the anti-British War. In the peace of Roma Nuova 1836, Britain had to cede its lands in South Atlantis, which were divided along the Tropic of Capricorn: Braseal went to New Rome, the Germans received Argentine as a place for settlement (from now on, more often called Argentinien). 1837, the first German settlers arrived there.