We rolled in around 10.30 and the place was surpsingly empty. It actually felt kind of nice to arrive before everyone else, we got to really apreciate the place before it filled up. Becuase, yes, it did. So, you cannot show up without having a reservation during high season - some people came and hoped to get a sunbed for the day, but were turned down - there simply wasn't any room to spare.
I booked our beds, facing the ocean, a few weeks ahead of our trip - I made the booking online here. We chose the PuroBeach club just south of Palma, but they also have another location on the island: Illetas. We payed €70 each, which felt pricey when we payed, but turned out to be so worth it after all! You have access to the pool, changing rooms with showers, bathrooms and we were also welcomed with fresh fruit, mineral water and a glass of Cava.