When in doubt or not sure what to do, you should consult with an experienced immigration attorney or contact the US consulate in your home country.
Child born abroad to Lawful Permanent Resident (LPR) may be allowed to board the plane to the United States, if the child was born during the temporary visit abroad of a mother who is a lawful permanent resident alien of the United States, provided that the child’s application for admission to the United States is made within two years of birth and the child is accompanied by the parent who is applying for readmission as a permanent resident upon the first return of the parent.
Child born abroad to an accompanying parent after issuance of an immigrant visa to the parent but prior to the parent’s initial admission as an immigrant may be boarded as long as the child has a passport or is listed in a parent’s passport and is in possession of the birth certificate.
Before traveling to the United States, it's a good idea to contact the U.S. embassy or consulate in your home country to obtain a transportation letter.
CBP guidance can be found here.