There was only two mass Exodus from Egypt in recorded history out side the Bible. Josephus wrote that 1 St.century bce historian by the name of Manetho wrote that the high priest of Akenaten the king who started monotheism. This high priest rose up maybe after Akenaten died and with the help of the Hykos and his army attacked the Egyptions. He later changed his name to Moses. He and his followers we're expelled from Egypt. Manetho also stated that the Hykos after being expelled from Avaris went to Jerusalem. The Bible story and the Jewish practice of pass over etc could have come from one if not both of these events.
And on another note, The city of Pithom may have been built by bricks and not stone, but not burnt bricks, the Egyptians didn't use burnt bricks.