Heat the oven to 400 degrees. Lightly grease a 9×13-inch baking dish.
Place the ground beef, diced onion, and diced bell pepper in a large nonstick skillet. Cook while breaking the beef into crumbles with a wooden spoon. Continue cooking until the beef is completely cooked and the onion and bell pepper have softened.
Drain off any accumulated fat.
Add the tomato sauce, ketchup, brown sugar, mustard, Worcestershire sauce, garlic powder, and black pepper to the skillet. Stir until everything is evenly combined.
Bring the mixture to a simmer and cook for 3 to 5 minutes. Remove the skillet from the heat.
Transfer the sloppy joe mixture to the prepared baking dish and spread it evenly across the bottom.
Scatter a little more than half of the shredded cheddar cheese over the beef mixture.
Arrange the tater tots over the cheese, using approximately 2/3 of the bag.
Sprinkle the remaining cheddar cheese over the tater tots.
Bake for about 25 minutes, or until the tater tots have turned golden brown.