I was looking for the New York and not the NYC. This past week I did make it to the National Archives in NYC and used the index. I was able to ID direct family and cousins, too. At least with a file number it makes it easier when one needs to pay 22 USD and wait! At least you know there is some type of record.
For the New York State it is best to work from the last name and go through the years. The early years (1880-1900)do not have data as much but after 1900 it picked up. In the NARA in NYC it is on microfiche.
It is too bad the state does not make it easier to use the index. They do now have the death index online from 1957 forward but looking for the earlier years for birth, marriage, and death.
For NYC there is some indexing done by the German Genealogy Group and the Italian group, both online. I have used them to locate the file and then order from NYC.
Thank you and happy family tracing,