Put the Tater Tots in a large microwave-safe bowl and microwave until slightly thawed, about 4 minutes. Let cool, then lightly mash with your hands. Stir in the egg and flour. Form the mixture into twelve 1 1/2-inch balls with damp hands.
Make an indentation in the middle of each ball and stuff with a mozzarella cube; form the Tater Tot mixture around the cheese to cover.
Combine the breadcrumbs and 1/2 teaspoon salt in a shallow dish. Heat 3 inches of vegetable oil in a large wide pot over medium-high heat until a deep-fry thermometer registers 350 degrees F. Working in batches, roll the balls in the breadcrumbs and fry until golden, about 8 minutes. Remove with a slotted spoon to a paper towel-lined plate to drain; season with salt. Serve with marinara sauce.