Make the soup: Heat the vegetable oil in a large stockpot set over medium-low heat, then sweat the onion and garlic together until they are extremely soft but not browned, about 5 to 7 minutes. Add the tomatoes and cook, stirring occasionally, until they are bright orange and have started to dry out, about 7 minutes. Add the stock, corn and squash and bring the soup to a boil. Cook until the squash begins to soften, about 10 minutes, then remove the soup from the heat and set aside to cool for 10 minutes.
Transfer the soup to a blender and blend until smooth. Return to the pot, season to taste with salt and pepper and keep warm.
Make the garnish: In a large pot, bring salted water to boil. Blanch the squash blossoms, if using, and summer squash vines for 1 minute. Transfer the blossom and vines to ice water, shock and drain. Pour the soup into each bowl and garnish with the blossoms, vines and tomatoes. Drizzle with chile oil and a bit of crema. Garnish with cilantro and serve immediately.