It helps to know that only a fraction of German sources have been indexed and thus can be searched on ancestry.com or familysearch.org. If your ancestor happens to come from one of those places whose records have been indexed, great. This is how you found Josef's wife - Hamburg is one of those places.
There are also a number of other sources (Protestant and Catholic church books, especially) that exist and can be looked at online (Protestant church books at archion.de, which is a pay site; Catholic church books at data.matricula-online.eu, which is free). But these sources are not indexed, so you need to know the exact parish to look in (as well as be able to read the old German handwriting). Again, not all church books are available here, but if you cannot find your ancestor at ancestry.com or familysearch.org, this is an alternative place to look.
But in order to have success here, you need to know specifically where in Germany your ancestor came from (and also what religion they were). I do not know what resources you have in Argentina for this, but for Germans who emigrated to the U.S., you can look at death certificates, immigration records, newspaper obituaries, or family papers.