Preheat a smoker to 250°F. Add the wood chips according to the smoker’s instructions.
In a large bowl, mix the ground beef, egg, breadcrumbs, sun-dried tomatoes, olives, oregano, garlic powder, salt, and black pepper. Mix gently until combined, taking care not to pack the meat too tightly.
In a small bowl, stir the softened cream cheese and milk until smooth and spreadable.
Place the meat mixture on a sheet of parchment paper and shape it into a rectangle about 1 inch thick. Spread the cream cheese mixture down the center, leaving a border around the edges. Use the parchment to help fold the meat over the filling, then pinch the seam and ends closed. Shape it into a loaf with the seam underneath.
Set the loaf on the smoker grate. Smoke until the center reaches 160°F on an instant-read thermometer, checking the temperature in the meat rather than the filling. Let it rest for 10 minutes before slicing so the filling settles.