It depends what stae you live in.In here in Alabama no you can't.
There is no state that will allow a student driver (Class CP) to drive without a person who is over the age of 18-21 in the car (the age of the other driver may vary). A Class D license will enable the underage driver to drive without a passenger,, but there are restrictions to places allowed to travel and curfews.
Not in California. Permit drivers MUST have a 25-year-old, California-licensed driver sitting in the front passenger seat at all times.