Could it be as simple as an air door shifting position? I know whether heat or cold, I do not get any circulation until a short delay after startup. If heat, and its a cold start, it is awhile. If its a warm start for heat, or a hot start for AC, then a 4-second delay sounds about right. All about not blowing the incorrect climate-adjusted circulation until the car says it's ready.
In other words, could very well be normal operation and a 'feature' not a 'bug'. Hope so.
P.S. I won't make any suggestions of parts to buy - figures I do it for you and that one time I was wrong? It's a shocker to me.
FYI I thought I was wrong once, but I was only mistaken.
