I guess the best way to do it would be by making a mesh of the sand texture of Your beach with quite of a dense grid. I guess by adding armature on vertex points and weight painting them accordingly for each armature bone, then the armature would need to be recorded with actions to move down for every bone. Also their individual sensors should be added that would detect 4 eg. the stick or a finger that would actuate the movement of the armature bone downwards.
To be honest i think for that You would need to use Monsters attractor Monster's manic gadgets - the attractor … for something added to the thing that makes empties to spawn and respawn to mouse cursors current position after every time it is being changed if the mouse is moved for adding the actuator that would move sand inwards on the perimeter.