Pour 1 cup filtered water into the Instant Pot, then insert the trivet. In a large bowl, combine the ricotta, Cheddar, Parmesan, zucchini, basil, oregano, black pepper, salt, mozzarella, and tomatoes. Mix thoroughly. Transfer this mixture into a well-greased, Instant Pot–friendly mug (or multiple, smaller mugs, if desired).
Place the mug onto the trivet, and cover loosely with aluminum foil. Close the lid, set the pressure release to Sealing, and select Manual/Pressure Cook. Set the Instant Pot to 5 minutes on high pressure and let cook.
Once cooked, let the pressure naturally disperse from the Instant Pot for about 10 minutes, then carefully switch the pressure release to Venting.
Open the Instant Pot, and remove the mug. Let cool, serve, and enjoy!