This should be done in a relay style where the large cup is at one end and the bucket of water is at the other. Cups should be at least 16 oz. You will be counting the number of trips it takes to fill the cup from the bucket. Be sure to have the bucket and cup the same distance for all rounds and all players.
You can try a variety of sponges. You can play against each other or teams and see who fills the cup first. You can designate a sponge type or let players choose a sponge type. It may be better to place the cups on a table so that player do not tip them so easily. Cups with wider bottoms will have fewer spills. This activity is best done outdoors on a level surface.