Depends on where you live in NY.
"No
ammunition shipped directly to anyone in any of the following counties:
Bronx, Kings, Nassau, Queens,
Richmond, New York."
Full list of Zip codes where its a no go here
(Bottom of page)
budsgunshop.com/feeds/state_reg/new_york_restrictions.pdf

Nicholas, no. New York allows you to buy ammo locally, but if you buy it online, you have to have it shipped to a local FFL. Some online vendors will not ship ammunition to New York. https://theprepared.com/self-defense/guides/where-how-buy-ammo/