Modern food isn't an "imitation" of older foods. It's just food.
That one in particular is still super popular. Go to the store, buy a pita. Brush oil on it and sprinkle with some feta or a mozzarella bake to melt the cheese but don't crisp the bread. Maybe grate some parmesan cheese. Depending on your store they might just sell it. Mine does, although technically focaccia is allowed to rise while early pizza/pitta wasn't.

And I hate to break into you, but bread is a processed food. So is oil. And cheese. You can't find a loaf of bread growing on a tree. You can't even find most of the ingredients in the wild: you pick the grass, remove the seeds, dry them, crush them into a powder while possibly removing some parts, and then mix it with other things, including but not limited to: the residue of seeds and nuts crushed into oblivion, processed and separated milk solids, and a hearty dose of preservatives (salt).

If you're going ancient you also need to add some sand, since the mills were so garbage they left sand in the food. The way it etched peoples teeth is part of how we can tell dietary makeup.