A child born abroad to a U.S. citizen parent or parents may acquire U.S. citizenship at birth if certain statutory requirements are met. The childs parents should contact the nearest U.S. embassy or consulate to apply for a Consular Report of Birth Abroad of a Citizen of the United States of America (CRBA) to document that the child is a U.S. citizen. If the U.S. embassy or consulate determines that the child acquired U.S. citizenship at birth, a consular officer will approve the CRBA application and the Department of State will issue a CRBA, also called a Form FS-240, in the childs name.
"The childs parents should contact the nearest U.S. embassy or consulate to apply for a Consular Report of Birth Abroad of a Citizen of the United States of America (CRBA) to document that the child is a U.S. citizen.'
It does not say "must" or "shall".
Here are the State department requirements for a child born abroad without a CRBA to obtain a US passport. A US passport is proof of citizenship.
Foreign Birth Documents + Parent(s) Citizenship Evidence
If you claim citizenship through birth abroad to U.S. citizen parent(s), but cannot submit a Consular Report of Birth Abroad or Certification of Birth, you must submit all of the following:
Your foreign birth certificate (translated to English),
Evidence of citizenship of your U.S. citizen parent,
Your parents' marriage certificate, and
A statement of your U.S. citizen parent detailing all periods and places of residence or physical presence in the United States and abroad before your birth.
https://travel.state.gov/content/passports/en/passports/information/secondary-evidence.html