Bring water to a boil in a large pot. Place pumpkin in a blender. Cover and blend until pureed.
Stir pureed pumpkin, beef, soup bones, and salt into the water; add beef broth, garlic, thyme, and ground black pepper. Cover the soup and simmer until until beef is nearly tender and cooked through, about 40 minutes. An instant-read thermometer inserted into the center should read 160 degrees F (70 degrees C).
Stir corn, carrots, potato, noodles, bitter melon, radish, Scotch bonnet chile pepper, and green onions into the soup; cook uncovered until vegetables are tender, about 10 minutes.