There was a Nathan Finkelstein who was the son of Morris and Rebecca Finkelstein - he appears in New York City
On the 1892 NY Census as Nathan Finkelstein - age 3 - born US - https://www.geni.com/documents/view?doc_id=6000000082711790850 - where he is the youngest of 8 children
On the 1900 Census as Nathan - born Sept 1888 - age 11 - self & parents born Russia - still in New York City, the youngest of 8
On the 1905 NY Census as Nathan - age 15 - born Russia
On the 1910 Census as Nathan - age 20 - self & parents born Russ - https://www.geni.com/documents/view?doc_id=6000000082711135983
On this 1912 NYC Marriage Record - https://www.geni.com/documents/view?doc_id=6000000026853415075 - where his residence is the same as it was on the 1912 Census
On the 1925 NY Census, his wife appears as Kate Fink with a son Stanley, age 4, and her mother, plus 3 more who are really her brother, her brother's wife, and her brother's daughter. Nathan is not there.
On the 1930 Census, his wife appears as Kate Fink with a son Stanley R, age 8 - and she is listed as a widow. Living in New York City.