The link is clearly from Adoption part of USCIS - so wouldn't have been applicable to your child. All you had to do was complete the DS-11 form (and gotten his birth father to complete the form as he was absent but consent(ed) to US passport issuance, get it notarized), booked an appointment with either local post office or special issuance agency if you had to return urgently after arrival to the US and gotten the child US passport.
Green card only comes if you've actively done your part which is paying the USCIS green card issuance fee - not required for minor children who will become citizens after entering the US with immigrant visa.