Since you received your green card in Jun 2024, you became a "U.S. person" and your worldwide income are subject to U.S. federal income tax return. You will report your German wages and other income on a Form 1040, the income tax you paid to the German revenue office on the same income could be used to offset your U.S. federal income tax return, using a form 1116. There is also a Foreign Earned Income Exclusion, use Form 2555 for that. I would think TurboTax should be able to handle all that, though I do not have any personal experience using TT for expats.
I suspect the German tax rate are higher than the U.S. That means you may not owe the Internal Revenue Service anything and the filing would only be a formality. Assuming you did not live in the U.S. during 2024, there is no need to file a state income tax return.
You said you came to the U.S. in April 2025. If you arrived after April 15, 2025, then your Form 1040 would not be due until June 15, 2025. TT should be able to insert a header at the top of Form 1040 that you were out of the country on April 15th. If you arrived before April 16 and did not file an extension request, Form 2848, then you should file your 1040 asap.
Take a look at IRS Publication 54, linked below. Also, read the U.S. - Germany tax treaty. Good luck!
Publication 54 (2024), Tax Guide for U.S. Citizens and Resident Aliens Abroad | Internal Revenue Ser...
Germany - Tax treaty documents | Internal Revenue Service
