Heat oil in a large saucepan over medium heat. Add the onion, the garlic, 1/2 teaspoon salt, and 1/4 teaspoon pepper, and cook until softened, about 5 minutes.
Add the tomatoes with their juice and the thyme; simmer, stirring occasionally, until the sauce has thickened, 20 to 25 minutes.
Sauce can be frozen for up to 2 months.
To make a meat sauce, use 1 pound cooked ground meat, such as beef, sausage, turkey, or pork, and add to sauce along with the tomatoes.