Preheat oven to 450°F. In a large bowl, combine potatoes, oil, paprika, salt, pepper, cayenne and thyme; toss well to coat.
Divide potatoes between 2 rimmed baking sheets, spreading in a single layer. Bake for 20 minutes. Remove pans from oven and flip potatoes over. Sprinkle with garlic. Return pans to oven and bake 20 minutes longer.