As an archangel, St. Michael is not truly described to have been "born" in the human sense. Instead, God created the angels before time and outside of its confines.
It is difficult to determine from scripture exactly when God created the angels. Time itself began existing as a human construct with the creation of humans. Angels, created by God, existed before time itself did, according to GotQuestions.org.
St. Michael is described alternatively as an archangel or as a prince of angels. The Epistle of St. Jude indicates that St. Michael leads God's army in the battle against Satan's army in the final fight for humankind and the Earth.