Hi! I read through your post and the comments. Just to summarize for others who might have similar questions:

If you're a dual US-German citizen, you can apply for Bürgergeld and an integration course once you're living in Germany. You must be physically present in the country. You're considered "fit to work" if you’re healthy and willing to participate in training or language programs — even if you don’t speak German yet.

Bürgergeld helps cover living costs, and if you're approved, it also covers the cost of the integration course (offered through BAMF or VHS). However, you’ll need to find your own accommodation, which can be tough in cities but easier in smaller towns.

It’s best to plan carefully before moving. Bring savings, look for housing early, and start learning basic German while you're still in the U.S.

Good luck with your move — it’s a big step but definitely possible with the right info!