You can get to the Ocean by Boat. You can go up to Ponce Inlet and then out into the Atlantic Ocean. It is about an hour boat ride to the inlet.
You can boat up to the back side of the beach and walk over the sand dune to the beach. There are two locations where this can be done.
The first is to, go south past channel marker 17 and then turn east and follow the posts in the water. The posts lead you towards a buoy. Turn north before you get to the buoy until you are even with the parking area on your right. This last leg is fairly shallow. The parking area is the furthest south parking area for Apollo Beach. It is less than a 100 yard walk over to the beach and ocean. Please note that further south on this beach it is clothing optional.
The second option is to cut trough government cut and reach the barrier island near JB's restaurant. There is a boat ramp just south of here where you can cross over to the beach. Both of these locations are part of the National Park and you must pay for entry. If you don't have a pass, the entry booth to pay is in the road near this area. Look for the large flag.