The facts don’t need CBRA paperwork to substantiate them, as the Birth Certificate does that.
As far as the USG is concerned the CRBA issued by the State Department IS the birth certificate.
Negative.
7 FAM 1441.1 (State Department Manual)
f. The Form FS-240 is not a birth certificate, such as is issued by a government- authorized bureau or office of vital statistics, because consular officers are not authorized to assume a foreign local or state vital statistics function. The Form FS-240 is a consular declaration of the fact of acquisition of U.S. citizenship at birth ...