A simple solution
You can achieve similar results by opening all doors for about ~1 minute before entering your car. All hot air inside the car will be replaced with probably still warm air from the outside. If there's no wind, you can turn on the ventilation addtionally. One minute of ventilation usually won't hurt the car battery too much. Plus, it get's the heat out of the ventilation system as well.
The problem isn't as much the inside air as the car itself
The car's roof and seats will still be heated up. The warm air from the outside will do little to actually cool them down. Air is a bad thermal conductor. It is thus not good at cooling things down. For reference feel how hot the street gets on a summers day. And the street is outside all day with warm air replacing heated air, which rises up. You can actually see how the air rises. It's the haze on hot days.
In conclusion, the incoming heat from the sun is just too much to dissipate via environmental air cooling.
For better results
Put reflecting foil in all of your car's windows. Stow it away in the ~1 minute you have all doors open. The foil will keep the heat out of the car in the first place. So the interior won't be heated up that much.
Still better results can be achieved in the same ~1 minute time frame: Pour water over the roof. The water will evaporate and cool the roof a bit. You should do that before stowing the reflective foil, so the evaporative water cooling has some time to take effect. This easily takes the roof from "don't touch" to "still warm".
Everything is about money
With the above options, how many people do you think would pay $$$ for a technical solution that will probably mitigate the problem worse than above?
If $$$ doesn't matter for your technical solution, have a look at how absorption refrigerators work:
You could basically use incoming heat (e.g. from a black panel on your car's roof) to turn your car into (sort of) a fridge. It will most surely not get as cold as a real fridge but the principle is sound. I'd assume that the overall efficiency might suffice. This assumption is based on eliminating the need to convert energy from the sun to electricity and use that to transfer heat energy. Instead you'd use sun energy quite directly to power the process.
However the amount of plumbing and the simple fact that the heat should best be applied from below, while coming in from above, makes this system at least troublesome to implement for mobile applications like cars.
There are multiple concepts, none of which is too few a hassle in terms of price, efficiency and usability to be widely implemented.