Nevada Beach Campground doesn't open until May 12, 2017. It's closed for the winter.
Looking at the list of sites, there is lots of availability depending on how long you want to stay. Weekends fill up soonest.
Are you just looking at the "campsite list" or the "date range availability" below the map of the campground? The "date range availability" tab will give you a list of all the campsites and will show what dates each are available. You might find you will have to change sites mid-stay to get the dates you want.