There was plenty of German immigration between 1810 and the civil war: https://en.wikipedia.org/wiki/German_Americans#19th_century

Also, I have no idea why you think it relevant that they were European. Certainly Ben Franklin didn't: http://www.theatlantic.com/politics/archive/2008/02/swarthy-.... At the time of actual immigration, the majority opinion was not that Italians, Poles or Jews were desirable immigrants.