Essentially, 8 AM is the earliest time you can purchase beer on Sunday in New York state.
In New York alcohol sales are not permitted between 3 AM and 8 AM on Sundays for consumption off-premises, while on-premises sales are not permitted between 4 AM and 8 AM on any day.
However, each county in NY State may have slightly different alcohol rules. See individual county closing hours for Liquor, Wine and Beer here: http://www.sla.ny.gov/provisions-for-county-closing-hours
Liquor stores are also required to close one day per week, on a day of the store's choosing.
Prior to 2006, off-premises alcohol sales were forbidden until noon on Sundays, and liquor/wine stores were required to be closed the entire day. Because grocery stores are not permitted to carry wine or liquor, the older law essentially meant that only beer and alcoholic malt beverages could be purchased at all on Sundays.