The first 3 digits of a zip code represent the sectional center facility code, the smallest of which is 005. One would assume that 00501 is the smallest zip code (which apparently maps to HOLTSVILLE NY )

http://pe.usps.com/text/LabelingLists/L002.htm#xd_L002

https://tools.usps.com/go/ZipLookupAction!input.action