First, I must say that vital records in the present New York City are not included here. I never have had to try to get any vital records from NYC. Check elsewhere on the net for NYC vital records.
Most people assume that since New York State was one of the original thirteen colonies that there should be vital records beginning in the 17th century. That is not the case. When New Amsterdam (later New York) was a Dutch colony, the government didn’t record vital records. Instead, the Dutch assumed that vital records would be recorded by churches in their records. The English took over in 1664 and renamed the colony; New York. They did have a law that said churches should record vital records but never enforced that law. Colonial vital records are very rare. A few towns on Long Island did keep some vital records for a while but slowly over time they discontinued the practice. There is a book; New York Marriages Previous to 1784, which appears to contain marriage records of people that were not married in a church. The book was originally published in 1860 but Genealogical Publishing has republished the book with an additional 100+ pages. The book is currently of print but you should be able to find a copy in larger libraries or online used book stores.
There was an early attempt to begin vital registration in 1847, when the clerk of each school district was to collect the birth, marriage, and death records and report them to the town clerk. That system failed as many communities did not comply because there was no enforcement of the law. The entire system was abandoned about 1851. Some of those records have survived. New Horizons Genealogical Services has this web page with links to those records which are online. More of those vital records are in county courthouses, town historians, historical societies and other places. Finding them is difficult to say the least but might be worth the search if you are looking for those few years.