Add barley to saucepan or pressure cooker with 2 cups water and a pinch of salt. Pressure cook on high for 15 minutes, or simmer for 40 minutes in a saucepan, until soft. (Add more water if required due to evaporation.)
Cook the soup
Heat olive oil in a large soup pot over medium heat or use the sauté function on your pressure cooker. Add garlic, and sauté until slightly browned.
Add onion and sauté until translucent. Add celery, carrots, fresh thyme, and bay leaves. Sauté 10-12 minutes to soften and infuse the flavor of the thyme into the vegetables.
Add water, tomatoes, green beans, salt, and optional sugar, and bring to a boil. If the barley is cooked, add it at any time, along with the cooking water. Reduce heat, and simmer for 30 minutes, or pressure cook on high for 8 minutes. Cook until the vegetables are soft.