Unfortunately, I am having trouble finding books specifically about German-Jewish immigration to the US that’s NOT related to the Nazis and the Holocaust. These books are set after 1933, which isn’t the time period that I’m interested in.
I did find a wonderful book called Branching Out: German-Jewish immigration to the United States, 1820-1914 by Avraham Barkai, but unfortunately the book is only sold as paper copies. I’ve placed an order for a copy of the book, but I want to know if there’s any other books available on this subject, preferably available as e-books for Amazon Kindle.
Probably the first book you want to check out is A Time For Gathering by Hasia Diner, as its time period includes literally exactly the specifically German wave of Jewish immigration to the US (1820-1880).
Further reading could include Emerging Metropolis by Annie Polland and Daniel Soyer, part of the City of Promises trilogy- a history of the Jews in New York. The book starts in 1840, and so should cover the years of German immigration pretty thoroughly. (Jewish New York is a condensation of the trilogy that also has a decent section on German immigration specifically, but Emerging Metropolis probably covers it in more depth.) City of Promises by Moses Rischin is always a good general starting point as well when discussing Jewish immigration to New York, though it starts in 1870 and so doesn't necessarily cover much of the specifically German immigration to the same extent.
I recently came across the book, Bread to Eat & Clothes to Wear: Letters from Jewish Migrants in the Early Twentieth Century by Gur Alroey. It's not specifically focused on German Jews as such, rather Central and Eastern European Jews migrating to the USA between 1900-1914. However, it may give you some idea (using primary documents) of what Jewish immigrants faced when arriving in the USA pre-World Wars.