I don't see anything that would stop the child from entering.
The airline will board the child on the basis of the green card
When arriving at the US port of entry, the child will be able to enter because there are only two possibilities:
The child is a US permanent resident, in which case they can enter on the green card
The child is a US citizen, in which case he/she cannot be denied entry to the US no matter what, regardless of whether he/she has the required documents or not