Grease a 4- to 6-quart slow cooker with 1 tablespoon of the olive oil. Add the zucchini noodles to the slow cooker, making a well in the center.

Add the feta cheese and tomatoes in the well. Drizzle the remaining 2 tablespoons olive oil over ingredients over the zucchini noodles, cheese, and tomatoes.

Sprinkle the garlic powder, dried oregano, sea salt, and black pepper over the zucchini mixture. Add the thyme sprigs. Cover and cook on LOW for 4 hours.

Mash the feta cheese with a fork. Stir the noodles and the cheese together until all ingredients are combined. Stir in the olives just before serving. Garnish with additional thyme sprigs, if desired.