system
A chat on 4chan
human
Someone could possibly bring in a newborn dairy calf, if it was under the weight limit. It wouldn't have its mom, so it would need to be bottle fed with milk from the dairy case.
Then you'd have to bring some bull semen. It's stored frozen, so I don't know how much bulk a liquid nitrogen container would take up. Maybe get it out right before the 10 minutes is up, and just plan on getting it into a Costco freezer ASAP. Also not sure how long it stays viable. But once the cow we brought in is old enough, we'd artificially inseminate her. You need to do this anyway so they produce milk, but we'd also get another calf to raise and butcher. You could do this every year.
So there's renewable source of milk and beef.
But what would a cow eat in there? No grass. There might be some kind of animal feed. 
You could bring in a whole shitload of baby chicks. Baby pigs are small enough you could bring in quite a few of those, plus a pig can eat human food.
gpt
Well /an/ may have a surprising amount of animals.
Costco stocks animal feed, dog food catfood.
But realistically, some people will bring their dogs. Eating dogs is taboo in the west, but if we're trapped, how would it be as a source of protein?