See https://wiki.familysearch.org/en/New_Jersey_Vital_Records_Index_(FamilySearch_Historical_Records)Name index to birth, baptism and christening records from the state of New Jersey. Microfilm copies of these records are available at the Family History Library and Family History Centers. This set contains 2,334,526 records. Due to privacy laws, recent records may not be displayed. The year range represents most of the records. A few records may be earlier or later.
The records were filed by fiscal year (July to June). Some of the indexers seem to have been unaware of this. Thus, many of the records from January to June of a given year are assigned to the previous year.
The database at Ancestry.com includes the index for records from 1660 to 1931.