Today’s German genealogy tip of the day is this: Germans almost always chain-migrated to America. If you have a German immigrant ancestor, bet on the fact that several of their close family members also immigrated to America, probably both before and after your ancestor. Readjusting to a new country, a new way of life, and a new language would have been difficult, and many Germans wouldn’t have undertaken such a radical change in lifestyle if they didn’t have some piece of home waiting for them in the New World. Immigration was also a costly process, and relatives who had already gone to America and become successful could send some of their savings to family members back in Germany to help them with the emigration process.
To find who the other immigrant family members of your German ancestor were, try checking the area (usually the counties) where your immigrant ancestor lived in America for other people with the same surname. Investigate those same-surnamed people in close proximity to your ancestor and see if you can establish a relationship. For someone with a common last name like Schmidt or Meyer, it might be difficult to wade through all of the unrelated families with the same name in a wide area, but for a very rare surname, like Körzel or Rathsam, you might be able to investigate all of the families with that surname in the entire state, or the entire country.
Also try contacting the state archive in Germany in the province where your ancestor was from and ask if they can tell you the names of some of the other individuals with your ancestor’s surname from your ancestor’s hometown who are also recorded as having emigrated. Then you can try to find where in America (or Canada, Australia, Argentina, etc.) those individuals ended up.