Preheat oven to 350 degrees F. Oil a 6 to 8 cup shallow baking dish. Pierce sweet potato skins and microwave until tender, about 4-6 minutes. Cool.
In a large skillet, heat oil over medium heat. Add onion and celery cooking and stirring until tender, about 5 minutes. Add garlic. Cook and stir 1 minute. Add beef. Cook and stir until it just begins to brown.
Stir in tomato sauce, Worcestershire, 1 teaspoon of the thyme and 1/4 teaspoon of the salt and pepper; bring to a boil. Transfer to baking dish; spread evenly.
Scoop sweet potato from skins into medium bowl; add margarine and non-dairy milk, remaining 1/2 teaspoon thyme and 1/4 teaspoon each salt and pepper. With electric beater, beat until smooth; spread over meat in baking dish.
Bake until bubbly, about 20-25 minutes.