Hi there,

First off, mods, I entirely understand if this isn't up to snuff and needs to be removed, but I had typed out almost an entire response to this before my computer crashed and I'm not in the mood to dig up all the citations I used the first time around, although I will gladly offer additional citations if needed or desired.

Since this question is asking about literally all of the Americas and I have much more experience with the US, I'll focus on North America and then briefly address South America which, to my knowledge, Germans came to in large numbers later. The tl;dr, though, is that despite German states never having colonized the Americas, a lot of Germans ended up in the Western Hemisphere.

I can't speak for the Spanish, French, or Portuguese empires, but German speakers have been present in the English colonies since basically the time they were founded. Germans before 1783 usually came over as indentured servants (though there was a sizable number of free Germans in New Amsterdam, which was obviously its own deal until the British takeover). The best sources for this are actually 19th century German-American historians, such as Franz von Löher, Friedrich Kapp, and dozens of others who devoted themselves to the study of pre-Civil War German America. They wouldn't pass muster as historical works today for many reasons, but they do cover the bare details of German migration pretty well. As Löher says (and it's hard to differentiate his argument from later who many copied him, but seems borne out by modern historians), colonial German migrants were mainly religious refugees. Löher overlooks, however, the large population of Germans who went to Pennsylvania because of that colony's active recruitment policies for European emigrants. I should note here that Germans going to Pennsylvania should by no means be conflated with the Amish; most were settlers from what is now northwestern Germany who came as farmers and were recruited to take up lands on the borderlands between the rest of Pennsylvania and various groups of Native Americans.

There is a myth floating around the internet and particularly around bad Facebook posts that says the US only decided by one vote to not make German the national language. I spent time footnoting why this is a complete and utter myth in my previous post that was lost, and am willing to do that again if necessary, but I bring this up mainly to emphasize that while there was a large German community in the US after independence, it wasn't that large.

The first large wave of German immigration started in the 1830s, and a huge one (that actually surpassed the Irish at the same time, per the NY Board of Emigration Commissioners records) occurred in the late 1850s. The 1830s wave resulted in cities such as Cincinnati have large German-speaking populations; by 1850, Cincinnati was around 30% German speaking, and had been hovering around 25% since 1820, though the numbers before 1850 are dubious. The surge in German immigrants led to many cities having German-speaking minorities that would be mind boggling for any non-English language speaking minority to have a presence in today. Milwaukee, per Kathleen Neils Conzen, was more that 50% German speaking in the mid-1800s. New York in 1860 was home to the third largest urban German speaking population in the world, after only Berlin and Vienna, as Stanley Nadel demonstrates in his book. Conzen is particularly compelling on this front. German immigrants made themselves known wherever they lived through setting a large part of the social calendar and making it clear that the city was not homogenous. It also helped that, until World War I, they were basically considered a model minority. The 180 on that was jarring in 1917, but until then, German-Americans were considered the "next best thing" next to Anglo-Americans.

Germany would not be unified until 1871, which meant that no concerted effort could ever be exhibited to send German-speakers out to North America. My own research actually indicates that to a very significant degree, individual German localities sent people out to go to the US to get rid of them, but that's not the same as colonization.

This is also the time that notable numbers of Germans went to Latin America, as Frederick Luebke covered in Germans in Brazil. I can't cover post-WWII German settlement in South America without a bit more research, so I'll refrain for now, but Luebke's work stands up very well.

But I will end by simply stating that German heritage in the Americas is so common because literally tens of millions (per Stefan Manz) of German speakers, or people who could be broadly defined as German, came to the Americas, and regardless of whether or not they were the primary agents of colonization, they would undoubtedly make an impact wherever they made their lives