Preheat the air fryer to 375°F (190°C).
In a medium bowl, combine ground turkey, Worcestershire sauce, garlic powder, onion powder, salt, pepper, and olive oil.
Gently mix ingredients by hand until just combined; do not overwork the meat to avoid toughness.
Divide the mixture into 4 equal portions and form into patties approximately 0.5-inch thick.
Press a shallow indentation into the center of each patty with your thumb to prevent bulging during cooking.
Lightly coat the air fryer basket with non-stick spray or oil.
Place patties in the basket in a single layer, ensuring they do not touch.
Cook for 10 to 12 minutes, flipping halfway through, until internal temperature reaches 165°F (74°C).
If using cheese, place a slice on each patty during the last minute of cooking.
Remove burgers and allow them to rest for 3 minutes before serving on buns.