Add the garlic and thyme. Cook until fragrant while stirring frequently, about 1 minute. Pour in the drained diced tomatoes and cook for a few more minutes, stirring often.
Warm the olive oil in a large Dutch oven or pot over medium heat. Once the oil is shimmering, add the chopped onion, carrot, celery, seasonal vegetables and a pinch of salt. Cook, stirring often, until the onion has softened and is turning translucent, about 6 to 8 minutes.