Child automatically gets US citizenship even if one parent gets Naturalized
I got my US citizenship just a month ago. One of the things that I was told at the oath ceremony was that my minor children automatically got US citizenship becuae of that, and I could simply apply for their US passport based on my naturalization certificate (i.e. attachments included at least - child's birth certificate, some proof of me being the parent, and my naturalization certificate ).
Were you not told these details at your oath ceremony?