To get the Beach Sign, acquire Pool Toy rewards from the Casey Skatie Event.

Once the Story Event begins, you'll have 3 days to make as much progress as possible and gather the Pool Toy rewards. These rewards must be merged into an Inflatable Dolphin (Level 6).

After that, activate the Inflatable Dolphin by feeding it Butterflies and Moths of varying levels. Once activated, the Inflatable Dolphin (Level 6) has a chance to drop Flip-Flops (Level 1).

Finally, merge the Flip-Flops all the way up to Level 12 to create the Beach Sign!