Heat a large pot over medium heat. Add the ground beef and cook until browned, breaking it up with a spoon as it cooks. Drain excess fat if needed.
Add the diced onion, sliced carrots, and sliced celery to the pot. Cook for 5 minutes until the vegetables begin to soften.
Stir in the minced garlic and cook for 1 minute until fragrant.
Pour in the diced tomatoes with their juice and the beef broth. Add the uncooked rice and dried thyme. Season with salt and black pepper.
Bring the mixture to a boil, then reduce the heat to low. Cover and simmer for 20 minutes, stirring once or twice, until the rice is tender and the vegetables are cooked through.