Preheat your oven to 350°F (175°C).
In a skillet, heat olive oil over medium heat. Add the diced onion and garlic, sautéing until they are softened and fragrant, about 3-4 minutes.
Add the sliced Kielbasa sausage to the skillet and cook until browned, about 5-6 minutes. Remove from heat and set aside.
In a large mixing bowl, combine the sour cream, milk, paprika, salt, black pepper, and thyme. Mix well to create a creamy sauce.
Lightly grease the baking dish with non-stick cooking spray. Layer half of the sliced potatoes on the bottom of the dish.
Spread half of the Kielbasa mixture over the potatoes, followed by half of the creamy sauce. Sprinkle a layer of shredded cheddar cheese on top.
Repeat the layers with the remaining potatoes, Kielbasa mixture, creamy sauce, and finish with the remaining cheddar cheese on top.
Cover the baking dish with aluminum foil and bake in the preheated oven for 30 minutes.
Remove the foil and bake for an additional 15 minutes, or until the cheese is bubbly and the potatoes are tender.
Let the casserole cool for a few minutes before serving.