Place chicken legs into a large stockpot; pour water over chicken. Add minced garlic, salt, and garlic powder.

Cover and bring to a boil over high heat. Reduce to a simmer and cook until chicken meat falls off the bones.

Stir in chicken bouillon cube until dissolved; add carrots, potatoes, zucchini, chayote, and white onion. Reduce heat to medium-low and simmer until carrots and potatoes are tender.

Stir chopped cilantro into soup. Simmer for 5 minutes.