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Leavened bread was a pre bronze age thing. The whole point behind passover unleavened bread is the refugees theoretically had no time to let dough proof (not that I think the Exodus actually happened). As long as you're dealing with something that has gluten, leavening it is trivial. Iron age armies would make rolls, proof them with sourdough starter, and cook them on skewers over an open fire while on the march. Coarse grain rye might take a day or more to proof with sourdough, but it'll be sweeter and easier to digest after.

When it comes to if you make flatbread or not, it's more a property of does the grain itself have enough gluten to even rise (which things like barley does not). Usually if it doesn't, you'd make a porridge with it, but keep in mind that even making a porridge takes hours to really break down the grain. Leavening is almost always available.