Lost babies Alien registration card?

[CIA]

What must one do when appling for a childs first U.S passport and the mother has lost the childs alien registration card and the the foreign passport to prove that the child entered lgeally.

the child entered when he was 2, in the 1980's and has never left the country

How would the mother prove the legal status of the child to the passport agency that the child entered as a legal permanent resident and IS NOT OUT OF STATUS????

The mother naturalized when the child was 6, and the child derived citizenship from the mother.

Does the US keep track of those who entered the country legally with the stamp on passport and or alien number?

Are there archives the mother can search to see if they have her sons name on record?

[CIA]

how can the mother find the son's alien registration number?

there are no immigrational paperwork for him because it was only the mother who naturalized before the boy turned 18, so theres only paperwork for the mother