Heat oil in a large stockpot over medium heat; add onion, green bell peppers, and garlic. Cook and stir until onion and bell peppers are tender, 2 to 3 minutes.
Mix hominy, diced tomatoes with green chile peppers, vegetable broth, enchilada sauce, black beans, kidney beans, green chile peppers, and olives into onion mixture; bring to a boil. Reduce heat to medium-low and simmer until flavors combine, about 20 minutes. Season soup with salt.
Place tortilla chips into serving bowls and top with soup. Garnish each bowl with sour cream and Mexican cheese blend.