Children born abroad

This is a question regarding USA law and thus should be asked on the USA forum.
But it is my general understanding that, if you visit a country you have citizenship of, you cannot enter it using any other country‘s travel documents. This is to prevent that other country from having diplomatic responsibility for you in your own country. That‘s why international rules forbid it - but then again, I wouldn‘t be surprized if the USA are flouting international rules here too ...

I don’t see that they can say anything against one traveling with a valid passport. And I agree that it is a risk to try to obtain a passport on short notice especially from the States.  Fundamentally, what Beppi has written is probably true but I think there is a legal detail being overlooked. Until one has contacted the US officials and gone through the process of having the child declared a citizen, he is not recognized as one even if the rules say he has a definite right to citizenship. What would be the other option if one can’t get an American passport on time? One cannot just take the kid and claim he is American because of birth-right without obtaining the proper document which is a passport. To be sure, one should probably call the US consulate. But think about the scenario, the mother goes through passport control with the kid and presents herself and the kid with German passports. Why should they even question if the kid is eligible for an American passport? Presenting a valid passport cannot be seen as fraud when one doesn’t have another.