Self-centering (or lack thereof) in park and camber / caster / toe settings

All of the suspension geometry settings (caster, camber, toe) would require the car to be rolling to induce a pull. With the car stationary the static alignment settings can't do anything to cause the steering wheel to turn.

So, that's a power steering issue. It starts the moment the engine starts, which is also the moment the power steering pump sends pressure to the steering box.

That specific symptom is almost always a mis-centered valve block on the steering box like described in #3.