Heat olive oil in a large pot over medium-high heat.
Add ground beef and cook, breaking it apart with a spoon, until browned and no longer pink, about 5-7 minutes.
Remove excess fat from the pot, leaving about 1 tablespoon for flavor.
Add diced onion and minced garlic to the pot and sauté for 3-4 minutes until onions are translucent.
Stir in diced carrots, celery, and potato, cooking for another 5 minutes.
Pour in the diced tomatoes with their juice and beef broth.
Add dried thyme, dried oregano, and bay leaf. Stir to combine.
Bring the soup to a boil, then reduce heat to low and simmer uncovered for 25 minutes, or until the vegetables are tender.
Add frozen green beans and continue to simmer for 5 more minutes.
Remove the bay leaf, then season the soup with salt and black pepper to taste.
Serve hot.