Heat the olive oil over medium heat in a large pot or Dutch oven.
Add the diced onion and minced garlic, sautéing until the onion is translucent (about 3-4 minutes).
Add the ground beef to the pot, breaking it apart with a wooden spoon. Cook until it's browned and cooked through (approximately 5-7 minutes).
Drain any excess fat from the pot if necessary.
Stir in the chopped carrots, celery, and bell pepper. Cook for about 5 minutes until the vegetables begin to soften.
Add the diced zucchini, can of diced tomatoes (with juices), beef broth, frozen green beans, thyme, oregano, bay leaf, salt, and pepper. Stir well to combine.
Bring the soup to a boil, then reduce the heat and let it simmer for about 30 minutes, stirring occasionally.
Remove the bay leaf before serving and adjust seasoning to taste.