In a large bowl, combine ground beef, minced garlic, minced onion, soy sauce, salt, and pepper.
Shape into 4 equal-sized patties, each about 4 inches in diameter.
Preheat the air fryer to 375F (190C).
Place 2 patties in the air fryer basket and cook for 4 minutes per side.
Immediately top each patty with a slice of American cheese after cooking.
Mix together ketchup, mayonnaise, mustard, relish, garlic powder, onion powder, and paprika for the sauce.
Spread the sauce on the hamburger buns.
Add lettuce, patties with melted cheese, tomato slices, and onions. Top with the bun.