Heat olive oil in a large skillet over medium-high heat. Add pork; cook and stir until browned on all sides, 5 to 10 minutes.

Stir water and bouillon cubes together in a large pot over medium-high heat until bouillon cubes dissolve. Add pork, rutabaga, carrots, and celery; bring to a boil. Reduce heat to medium-low; simmer until vegetables tender, about 40 minutes.

Stir hominy and kidney beans into soup; simmer until hominy and pork tender, about 30 minutes more. Season with salt and black pepper.