The only way for the German parents to become parents of a US born child through surrogacy is through an adoption process, pursuant to German law. Even with a California birth certificate indicating they are the sole legal parents, Intended Parents cannot override the applicable German law (Art. 19 Abs. 1 S. 1 EGBGB) and can therefore not establish German citizenship of the child pursuant to §36 Abs. 1 S. 1 PStG. OLG Stuttgart.
German couples are strongly advised to seek local counsel prior to undergoing surrogacy in the U.S.