In a large bowl, toss together watermelon, tomatoes, cucumber, red onion, almonds, kosher salt, and pepper. Set aside to marinate for about 1 hour.
In a blender, working in batches, purée vegetables and their liquid until smooth and creamy. Transfer soup to a large bowl. Whisk in sherry vinegar and olive oil and adjust seasoning with salt and pepper to taste.
Cover soup and chill in refrigerator for 2 hours or up to 3 days. When ready to serve, adjust seasoning again with salt and pepper to taste. Combine crema and chopped Calabrian chiles in a small bowl. Ladle chilled soup into bowls and garnish with crema mixture and diced vegetables (if desired).
