Exodus and Sourdough During Passover

I'm certainly no expert on Kosher laws, but I did find a reference to soft matzah via Wikipedia. They do indeed exist:

Soft matzah. Unlike the hard matzahs familiar to most Jews around the world, the Yemenite and Iraqi Jewish communities eat soft, pita-like matzahs, as was apparently the custom in most of the Jewish world until recent centuries. In fact, many rabbis permit these matzahs to be eaten on Passover even today; the reason why they have gone out of mode is not a Halakhic [Jewish legal] one, but rather a technical issue: In the pre-freezer period, they did not retain their freshness and softness for more than a day or two, and therefore were customarily baked on Passover itself – when even a “drop” of chametz disqualifies an entire matzah. However, now that there are freezers and soft matzahs can be baked before Passover – when a “drop” of chametz that might fall into a dough is “batel b’shishim” (less than 1/61st of the whole and therefore nullified) – such matzahs would be kosher. They must not be more than approximately a centimeter thick, however; one should consult a rabbi for precise instructions.

It would have been something more like a soft baked unleavened bread. The reason why Ashkenazim bake them into crisp crackers is because in order to be stringent they poke holes in the dough for a more thorough quicker bake.