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.
We have a Renault and it is similar. I don't listen to the radio. If I have any audio, it's either something from my phone or navigation (also phone, usually off).
The default on the car is to turn on the radio on engine start. No way to change it. No way to make it remember that the last time the car was used it was set to Bluetooth audio. Switching back to Bluetooth requires navigating through 3-4 layers of menus. Even when you turn it off, it randomly turns back on for no reason. :/
My 10+ year old VW: remembers which audio source was last used. Phone autoconnects via Bluetooth every time with no hassle. Volume is never an issue (real buttons that respond in a timely manner on the steering wheel). Off is off until you turn it on again (with a physical button).
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.