What event in the Old Testament marked the beginning of the Exodus of the Israelites from Egypt, eventually leading to the Ten Commandments?

The Passover began the Exodus. On that night the Israelites killed a lamb and marked their doors with its blood. The angel of death passed over their homes, and Pharaoh let them go (Exodus 12).

The Ten Commandments came later at Mount Sinai. The Last Supper belongs to the New Testament.