There are two ways to get a sponge and both of them require Ocean Monuments. Both of these methods give you a Wet Sponge, not a dry sponge which you need for the goal. Therefore, you will likely need to take a furnace with you to the monument to smelt it for the goal. Another possible method is placing it in the nether and mining it, but unless you feel very safe about holding the goal you probably won't be doing this.
Killing an Elder Guardian will always drop 1 Wet Sponge 100% of the time, meaning that you should have a 100% chance of being able to get this goal from any monument. Luckily, there is already another goal for exactly this, see Kill Elder Guardian.
Monuments can also have Sponge Rooms. Based on some rudimentary testing around 82% of monuments had at least 1 of these rooms. They connect only at the bottom, meaning that you are more likely to find them near the top of the structure. The most easily accessible sponge rooms are often beside the top elder guardian room (see highlighted areas), and also sometimes in the back of the monument, depending on how the Gold and other rooms generate. Other rooms can be hidden in the maze a bit too much to make them reliable. If you enter without Milk or TNT, you can mine into one of these sides to see if you can grab a quick sponge and rotate to Kill Elder Guardian in the top room if you get donged.