Pour water into a large stockpot over high heat. Stir in 3 cups tomato sauce, yellow onion, chicken bouillon, garlic, and 1 tablespoon dried oregano. Bring broth to a slow boil.
Combine ground beef, eggs, 1/2 cup tomato sauce, white rice, 1/4 cup cilantro, seasoned salt, 1 tablespoon dried oregano, onion powder, garlic powder, black pepper, and cumin in a large bowl. Squeeze mixture with your hands until thoroughly mixed.
Scoop 1/4 cup of beef mixture and form in a ball. Lower gently into boiling broth. Repeat with remaining beef mixture.
Stir potatoes, carrots, and celery into the broth. Cover and simmer until meatballs and potatoes are tender, about 30 minutes. Stir in zucchini and cabbage. Cover and simmer until cabbage is tender, about 10 minutes.
Serve with a squeeze of lemon juice and garnish with avocado and 1/4 cup cilantro.