Are weddings on public beaches allowed?

I had the idea to have a ‘spontaneous’ wedding on a public beach at sunrise. It’s special to my SO and I bc we visit the beach at sunrise a lot. The beach is clean and typically void of people at sunrise. Since it’s a small wedding (25-30 guests) we wanted to find a venue to match. Most venues are out of our price range. But when I thought of having a sunrise ceremony on a special beach, I was excited and immediately it felt right. It’s close to where he lives now and my family wouldn’t mind the trip or the time. Someone would go ahead of us to set up a few rented chairs and maybe a wooden frame to serve as a backdrop. We’d be careful not to litter with any decorations or trash. Then at or before sunrise the wedding party would arrive followed by the guests. Maybe a short 20-30 minute ceremony. Then we’d tear down and head to a nice breakfast.
Of course I’d have a back up plan in case of weather. But this whole idea came together in about an hour and seemed perfect and I’m still so excited about the thought.
My question is concerning the legality of the situation. It’s public property. And even if it’s not strictly allowed, could I get away with having a short, 1 hour tops event in the wee hours of the morning? Any thoughts?