Preheat oven to 425 degrees F (220 degrees C). Arrange potato nuggets in a single layer on a baking sheet.
Bake in the preheated oven until light golden and crisp, 20 to 24 minutes.
Heat a large skillet over medium-high heat. Cook and stir beef in the hot skillet until browned and crumbly, 5 to 7 minutes; drain and discard grease. Add sloppy joe sauce and simmer until heated through, 5 to 10 minutes.
Arrange potato nuggets on a plate; top with sloppy joe sauce and Cheddar cheese.
