Preheat oven to 275°F. Spread tomatoes onto a large rimmed baking sheet. Add oil, salt, pepper, and garlic; toss gently to coat. Tuck thyme sprigs into mixture. Bake at 275°F until tomatoes are wilted but not all have burst, 1 1/2 to 2 hours.

Cool tomato mixture to room temperature; discard thyme. Store tomatoes with oil and accumulated pan juices in an airtight container in refrigerator up to 2 weeks, or freeze up to 2 months.