How can I make breadcrumbs without a full, yeast-leavened loaf of bread?

Three substitutes come to mind:

1. Saltine Crackers
2. Pretzels
3. Select brands of Cereal (Chex, Corn Flakes, etc.)

Take these for a spin in your food processor till you reach the consistency you desire.

Depending on your ultimate goal one or any of these could serve as a suitable sub for "bread crumbs"

Dry biscuits (American 'biscuits' - not cookies), or anything other flour based quick bread that dried out - if you're trying to replicate the bread crumbs. You may be able to get by with a modified muffin recipe as well. You'll want to avoid fats and oils to reduce the moistness.

Yeast bread develops a particular flavor and larger hole structure than quick bread though. The flavor of a quick bread breadcrumbs should be slightly different, but in many dishes the subtle difference won't be overwhelming unless the breading is a 'star' of the dish. The hole structure really doesn't matter luckily - as developing that is a large part of the time factor of real bread.

Drying it out will be the harder part. The denser structure holds moisture better, so slice it thin and give it low, dry, long heat.

_{Personally, anything that you're going to make for the purpose of breadcrumbs that isn't just a substitute (like cereal, crackers, etc in the other answer), sounds like it'd be easier just to make a loaf of fast rise bread to me.}

Hardtack. Or any other kind of plain, baked cracker.

Hardtack is baked from a simple dough made with flour, water, and salt. It is rolled out, and baked till brown into a kind of cracker. It is often twice baked, to remove all moisture for long term storage - depending on the moisture of the dough, how thickly it's rolled, and the kind of breadcrumb you need, this might not be necessary, or might be helpful. Many are rolled thicker and baked longer if they're intended for storage - but if you roll it quite thin, like a cracker it will bake quickly to the right texture, and if it's dry it should crumble easily into something like breadcrumbs.

Alternatively, you can pick any recipe for dry crackers or plain unleavened biscuits (think European style, not American). Hardtack is the simplest of these types of recipes, but some have more ingredients (sugar, salt, oil) if you want a bit more flavor in your breadcrumbs, or if you want to use a little leavening you should end up with a lighter texture.

The crumbs you get will be similar in texture to using saltines or pretzels, a little bit hard, dense, plain. But they'll work pretty well for most recipes, and you can make them with whatever flour you've got at hand. They're also pretty quick to make and very simple - one of the cracker recipes quoted a half to three quarters of an hour for a batch. One of the hardtack recipes suggested baking times of as little as 5 min per batch (depending on how thin it is), and the mixing time of the simpler version is not much more. Since they're already dry and hard, and need very little extra processing (~45 seconds with a mortar and pestle per mortar volume) I expect you'd have your 5 cups of breadcrumbs ready within 45 minutes of starting your recipe.

You might also get away with a simple bannock or flatbread, with the dough rolled very thin and pan toasted until crisp and dry. It depends on whether toasting them singly on the pan is quicker than all at once in the oven. These will tend to be softer, usually with a bit more fat (oil or butter) and may include more breadlike flavors (including yeast). The better flavor profile may be worth the extra time drying, depending on the recipe.

A couple of years ago I started an apprenticeship and studied at Tafe.
One of the first things I learnt was how to crumb a chicken schnitzel with Panko bread crumbs. I am frustrated with myself for loosing my recipe but you can make them without a loaf of bread. Not sure of the ingredients exactly but we used flour and seasoning of choice and and added butter while rubbing the mix gently between the fingers until we had a soft dry mix.