Preheat oven to 350°F. Spray a 9x13-inch dish with paleo-friendly oil.
Peel and cube sweet potatoes. Place in a large pot of water and bring to a boil. Let cook until fork-tender. Drain and return to pot. Mash with coconut milk, salt, and pepper. Set aside.
Heat olive oil over medium-high heat in a large skillet. Add ground beef, onion, zucchini, and carrots. Cook, breaking up the beef, until the vegetables are tender and the beef is cooked through. Add garlic and cook until fragrant; only about 30 seconds. Stir in tomato paste, coconut milk, coconut aminos, dried thyme, salt, and pepper; mix thoroughly. Bring to a bubble and let cook until thickened.
Pour into the prepared pan and spread mashed sweet potatoes over top.
Bake in preheated oven for 15 minutes, until thoroughly heated through.