German salary and the Foreign Tax Credit
Lohnsteuer withheld at source, plus Solidaritätszuschlag and Kirchensteuer where it applies, generally exceeds the US tax on the same income. Form 1116 credits it category by category, and the residual US tax on salary is commonly zero.
Your Steuerbescheid is the cleanest evidence of tax actually paid, year by year — which is exactly what the credit needs.