Heat the olive oil in a large pot over medium heat. Add the ground turkey sausage and cook until browned, breaking it up with a spoon as it cooks.
Add the diced onion, sliced carrots, and sliced celery to the pot. Cook for 5 minutes until the vegetables start to soften.
Stir in the minced garlic and cook for 1 minute until fragrant.
Pour in the chicken broth and add the shredded cabbage and dried thyme. Season with salt and pepper.
Bring the soup to a boil, then reduce the heat and simmer for 20 minutes until the cabbage is tender.
Taste and adjust seasoning if needed before serving.