We know of no New York State law that would prevent you from purchasing auto insurance with only a permit instead of a full license. Not all insurance companies will offer car insurance to a person that is not fully licensed. For example the company that CarInsurance.com represents in New York requires that you have your active license before you purchase insurance.
Most insurance companies that do allow a permit holder to acquire auto insurance will require you to obtain a full license within a certain period of time after the inception of the policy and/or for you to have a fully licensed driver on the policy with you. If you are a minor living at home with parents and have just received your junior permit, it would be easier if you were placed on your parent's insurance policy instead of seeking your own coverage.
To find out for certain what the insurance laws are for permit holder in New York state contact the NYS Department of Insurance.