Heat a large skillet over medium heat and add ground beef; cook and stir until meat is crumbly, evenly browned, and no longer pink, about 10 minutes. Drain and discard any excess grease.
Heat olive oil in a soup pot over medium-high heat. Cook and stir green pepper in the hot oil until it starts to soften, 5 to 7 minutes. Reduce heat to low, stir in garlic, cumin, and chili powder, and season with salt and black pepper to taste.
Mix cooked ground beef and tomatoes into green bell pepper mixture, breaking up tomatoes with a spatula. Add 4 cups of water or enough to cover the ingredients, reduce heat to low, and simmer at least 2 hours to blend flavors.