You're definitely going to need BIAB
Do you have to mash? The biggest hurdle would be finding something with any appreciable diastatic power. If you can find a malted product, then you can use:
Quaker oats, polenta or corn grits, maybe some kind of un-preserved granola? Check the baking isle - maybe you could pick up some coarse-ground wheat/rye flour. Also look at cereal: you might find one that is made of puffed wheat (maybe even barley?). In the dry goods isle (rice, beans, etc.), you can use rice, but you'll be looking to add to malt/grain flavor.
To add sugars in the kettle, you can use honey, molasses, maple syrup, or any unrefined sugars from the baking isle.
Fruit will be a good source of sugar content. If you're feeling lucky, you can pick some over-ripe organic fruit for their wild yeast. I would stick with peaches, grapes, berries. And make sure you give it a good wash. Use lemon juice (or another organic, unpreserved fruit juice) to drop the pH of the "wort"/"must" below 4.5 before adding the over ripe fruit. This will keep out the enteric bacteria from unclean worker/shopper hands.
This actually sounds like a lot of fun... I'm really interested to see if you could find something to provide enzymes for a mash!