Yes, some Big Sur campgrounds in Andrew Molera State Park and the Los Padres National Forest offer first-come, first-served camping, but it is important to arrive as early as possible to secure one of these limited but extremely popular spots.
Nacimiento Campground and the Andrew Molera hike-in campground are the only fully first-come, first-served campgrounds in Big Sur. Along Highway 1, just two of Plaskett Creek Campground's 44 campsites are available on a first-come, first-served basis and Kirk Creek Campground also has two first-come, first-served campsites. It's always best to check availability and make a reservation in advance if possible, but for the best chance at a last-minute Big Sur campsite, try booking a Hipcamp stay.