Can you make your way to the paved A1A bike trail from here? Traveling through to see a friend would like to enjoy this natural setting, have a lunch then get some biking exercise.

There is a bike lane on A1A and the roads to the park and beach are paved. Be advised, since you mentioned having lunch, there are no food services in this area. Restaurants are 5-7+ miles from here. There are tables at the park if you choose to pack a lunch, but others may have acquired permits for them for private purposes. (Bar-b-q pit/grills are there for that purpose. )

Yes you can.