Follow the package instructions for the coconut pudding mix. Pour the liquid mixture into small ice cube trays or jelly molds for a fun shape, or into a shallow baking dish if you prefer to cut it into cubes later. Refrigerate for 2–3 hours, or until fully set.
In a medium pot, bring about 8 cups of water to a boil. Add the sago and cook uncovered for 12 minutes. Turn off the heat, cover the pot with a lid, and let sit for 5 minutes, or until the pearls turn translucent. Drain and rinse under cold water for 20 seconds to stop the cooking. Set aside.
If using boba tapioca pearls, cook according to the package directions until chewy. Drain and set aside.
Peel papaya, remove the seeds, and cut the flesh into small chunks. (Make sure to use more of the ripe papaya flesh as the outer layer of the papaya can be bitter.) Save about 1 cup of papaya chunks for later as topping. With the remaining papaya, add them to a blender along with evaporated milk and condensed milk. Blend until smooth and creamy.
To assemble, in a large serving bowl, add the coconut gel, fresh papaya cubes, coconut pudding cubes, sago, and boba tapioca pearls (if using). Pour in the papaya puree and coconut milk. Gently stir to combine.
Add ice cubes, give it one final gentle stir, and ladle into individual cups. Serve immediately while cold.