Thank you for that link. My question now is how long is that process
When you submit your application, you will be investigated. However long that takes is however long it takes. From the link FlyingRon provided, it states: "The time frame will vary depending on the complexity of each individual case."
You can request a temporary work letter, if you include an employment verification letter with your application.
If you have any questions that were not addressed in the link, you can call the New Jersey Division of Alcohol Beverage Control at 606-984-1520.