Or HaChaim on Exodus 12:39/אור החיים על שמות י״ב:ל״ט

1 מצות כי לא חמץ, unleavened breads because it was not leavened. The Torah means that the reason they baked Matzot was that they did not have permission to eat leavened bread; as a result they had to hasten in order to bake מצות. These loaves turned out to be matzot even though some time had elapsed between the kneading of the dough and the baking. Possibly, they kept the dough in motion in order to prevent it from becoming leavened. When the Torah bothered to graphically describe that "their kneading bowls were slung as bundles in their dresses over their shoulders" (verse 34), such a description would not be justified unless we were to learn something from it. Surely the Israelites had some other place where they could have carried their dough. The Torah wants to teach us that they deliberately vibrated the dough to keep it from rising. The process was facilitated by the fact that they had not added yeast to the dough in the first place. The Torah describes that the reason the dough did not have a chance to become leavened before the Exodus as being: "for they were being expelled from Egypt."