Heat olive oil in a large pot over medium-high heat. Brown the ground beef for 5-7 minutes, breaking it apart with a wooden spoon until fully cooked and no pink remains. Drain excess fat if needed, then set the beef aside briefly.
Add diced onion and celery to the same pot and sauté for 3-4 minutes until softened and fragrant. Stir in minced garlic and cook for 1 minute until the aroma intensifies, then add tomato paste and cook 1-2 minutes longer while stirring constantly.
Return the cooked beef to the pot and add beef broth, stirring well to combine. Bring the mixture to a gentle boil, then reduce heat to medium and let simmer for the next steps.
Add sliced carrots, chopped potatoes, thyme, oregano, and bay leaf to your hearty savory beef vegetable soup. Stir everything together and let the hearty soup simmer for 20-25 minutes until potatoes are nearly tender.
Stir in the green beans and diced tomatoes, then simmer for 10-12 minutes more until all vegetables are completely tender. Season with salt and pepper to taste, then remove the bay leaf before serving.