Bring water to a boil in a saucepan. Add quinoa and bring back to a boil. Reduce heat and cover; simmer until tender, about 20 minutes. Pour into a strainer; run cold water over quinoa to cool slightly.
Place a steamer insert into a saucepan and fill with water to just below the bottom of the steamer. Bring water to a boil. Add sweet potato and beet; cover and steam until tender, about 15 minutes. Add edamame; steam until tender, about 5 minutes. Drain and cool until running water.
Combine tomato, red bell pepper, spinach, red onion, balsamic vinegar, olive oil, lemon juice, garlic, and black pepper in a large bowl. Fold in cooked quinoa, sweet potato, beet, and edamame. Top salad with goat cheese.