Every so often a walk-in cooler unit comes up for auction when a restaurant closes. I'd love to get one for my yet to be built "trapping shack."
Rather than run the cooler on a genset for days ahead of time, I'd locate a local source of dry ice to pull it down from ambient temp. Keep the doors open when dealing with that much dry ice though, as it can cause a lack of oxygen in small spaces. When I was a medical courier, we used to get 300# of it delivered 2x a week and it was only $150 for the tub with delivery (that's been about 10 years though). A couple big blocks would chill down a deer pretty good, and then you'd run the cooler's unit to maintain that.
Of course if you had utility power, then it wouldn't need a generator. My shack will most likely remain off the grid indefinitely.