From the State Department's website: Documentation of U.S. Citizens Born Abroad
"...The birth of a child abroad to U.S. citizen parent(s) should be reported as soon as possible to the nearest American consular office for the purpose of establishing an official record of the child’s claim to U.S. citizenship at birth. The official record is in the form of a Consular Report of Birth Abroad of a Citizen of the United States of America..."
I’m certainly familiar w/ FS-240, but simply being born abroad to a foreign father & American mother isn’t sufficient to convey American citizenship.