Transmission

GM actually has a name for this problem It's called 4T60E morning sickness. Due to the fact that this happens most often the first time you drive the car in the morning or when it has been sitting a few hours. It is caused by excessive wear in the valve body of the transmission. Allowing fluid to drain out of the torque converter back into the transmission. Or a stuck or worn Reverse boost valve. While it's annoying waiting for reverse the trans will still work for a pretty long time. If it always does this when reverse is selected, or the forward shifts feel sloppy when you are driving you might have a band going out. This means it's time for an overhaul.

Make sure the transmission is filled to the proper level. If the car has over 60K and the fluid has never been changed you might consider that.....new fluid sometimes revives transmissions.... (I did not say "fixes")