Heat olive oil in a large pot or Dutch oven over medium-high heat. Season chicken breasts with salt and pepper, then sear until golden brown, about 3–4 minutes per side. Transfer to a plate and set aside.
In the same pot, reduce heat to medium. Add diced onion and cook until softened, about 4 minutes. Stir in garlic, cumin, smoked paprika, and chili powder, cooking for 1 minute until fragrant.
Pour in chicken broth, enchilada sauce, fire-roasted tomatoes (with their juices), green chiles, black beans, and corn. Bring to a gentle simmer, stirring to combine.
While the soup simmers, shred the reserved chicken with two forks. Add the shredded chicken and cubed cream cheese to the pot. Stir continuously until cream cheese is fully melted and soup is creamy. Simmer for 10 minutes, or until chicken reaches an internal temperature of 165°F (74°C), to meld flavors. Adjust seasoning to taste.
Ladle the hot soup into bowls. Top generously with shredded cheddar, a dollop of sour cream, crispy tortilla strips, avocado, cilantro, and a squeeze of fresh lime juice.