A child that has at least one German parent automatically acquires German citizenship at birth. The place of birth is usually irrelevant.
However, it is important to note that if the German parent was born abroad after December 31, 1999, the birth of the child must be registered in Germany before the child reaches the age of one so that the child acquires German citizenship.
If a German national is born abroad, the birth can be recorded in the birth register at the competent registry office in Germany upon application, after which a German birth certificate can be issued.
However, depending on the family constellation, there are still a few things that need to be done before applying for a passport.
Learn more here.