If you haven't already, you should order a copy of his birth certificate from NY city as it sometimes contains informatin different than what the NY Foundling Hospital had in their files. Here is the information you will need to order his birth certificate, Ambrose Kearns 29 Mar 1900 13545. The 13545 is the certificate number.

I came across you post b/c my grandmother was adopted out of the foundling hospital too and I thought the Kearns name might be connected to my grandmother.