At the moment I can't find where to locate the cooking pot for cooking.
Early game, before you can craft a forge (and assuming your trader doesn't have a working one), you can find cooking pots in POIs pretty easily (subject to the whims of random numbers of course).
Step 1: find the kitchen in a POI
Step 2: loot all the things
Within a couple/few kitchens you ought to have at least a cooking pot, if not also the cooking grill. And lots of glass jars and canned food and maybe a wrench or two.
ETA: when I'm solo, I prefer
not to take the POI designer's preferred path through the POI (as denoted by lights pointing the way), instead choosing to bash through the windows of the kitchen (or bathroom - medicine cabinets are a prime target), take out the one or two sleepers therein, loot and go. When I'm co-op, then I
still prefer to thwart the designer's strategy for killing me, but my co-op partner is a boot-licking rules-follower so we tend to follow the "right" path to our doom. It's like he's never seen a zombie movie...