This is exactly what we did in Pakistan when it was over 40C (over 100) outside and could be over 55C (you don’t wanna know) in the car.
We would drive the car with windows open for a few minutes before trying to use the AC.
This was 30+ years ago when car ACs on the underpowered cars we had weren’t all that great. So YMMV on modern cars in the US.
It doesn’t need to be. Refrigerated items can be left out at room temperature for a while without sacrificing any quality while it’s more important to keep frozen items from thawing.
In short trips, it probably doesn’t matter that much anyway, but it’s interesting to think about.
As Taiwan can get really hot in the summer, we take steps to keep the interior temperature from getting that hot. One is that use reflective shields
for the car. Another is to leave the front windows down just slightly to allow air flow. They are higher than the car window rain guards so it’s not obvious but it does allow ventilation.
Then we do the same to start the car with all the doors open, the windows down and the AC high for a couple of minutes to lower the temperature of the interior. It works for us.
I thought we were talking about icecream. I was pointing out that car airconditioning wouldn’t come anywhere near keeping it frozen, even if I put it in the more rapidly cooled area.
And while, say, cream and milk won’t become immediately spoiled if they’re at room temperature, or even fairly hot room temperatures, for less than a couple of hours, IME it affects their storage time much sooner than that. I don’t do errands very often, so I need what I buy to keep for some time; and I often have multiple errands on one circuit. The first stop at which I might get milk could leave it easily riding around for long enough to screw up its storage; sometimes even for over that two-hour period, before I get it home and into the fridge. But it’s fine in the cooler; it’s fine even if I forget the icepack as long as there are several cold things going in there, even if the cooler had been sitting in a hot car. If I’m getting icecream in hot weather, it needs to be the last stop and I do need the icepack.