Dear Mr. Newton,
Thank you for posting your request on History Hub!
According to the German Missions in the United States website, if you are a U.S. citizen and if you were born in a U.S. Military Hospital, your birth was not registered with German authorities (i.e. the registrar's office). This means that German authorities cannot issue a German birth certificate to you at all.
Since the U.S. military does not issue birth certificates, parents are expected to report the birth at the nearest U.S. embassy or consulate as soon as possible. A Consular Report of Birth Abroad (CRBA) can be issued as an official record of the child’s claim to U.S. citizenship or nationality. For records relating to births after 1938 of American citizens in a foreign country, please contact the Department of State, Bureau of Consular Affairs. Also, for more information about CRBA, see Birth of US Citizens Abroad.
We hope this is helpful. Best of luck with your family research!