My car has this problem, only sometimes it takes a lot longer than two seconds.

The car when started always turns on the radio at the last volume the radio was on at, regardless of whether it was on when the car was turned off.

More than once, I have turned it on, and it was playing at full volume the Sirius FM ads, and would not lower the volume or turn off ( via the other physical buttons) for at least half a minute. I've done some damage to the volume button after that, and I have taken to just getting out of the car until the stereo responds.