What day did the Christian Church begin?

Answer 1

Catholic AnswerThe Catholic Christian faith emanated from God from the beginning of time, and was established on earth definitively from the side of Jesus Christ on the cross outside of Jerusalem when He side was pierced by a spear, around 33 A.D.. Then it was shown to the world at Pentecost with the coming of the Holy Spirit, fifty-three days later.

from The Catechism of the Catholic Church, second edition, English translation 1994

766 The Church is born primarily of Christ's total self-giving for our salvation, anticipated in the institution of the Eucharist and fulfilled on the cross. "The origin and growth of the church are symbolized by the blood and water which flowed from the open side of Christ as he slept the sleep of death upon the cross that there came forth the 'wondrous sacrament of the whole Church.'" Sacrosanctum concilium 5) As Eve was formed from the sleeping Adam's side, so the church was born from the pierced heart of Christ hanging dead on the cross. (Cf. St. Ambrose, In Luc. 2, 85-89: J.P. Migne, ed., Patrologia Latina {Paris: 1841-1855} 15, 1666-1668)

Answer 2

When Jesus rose from the dead and appeared to the apostles.

Answer 3

The Church began on Pentecost about the year 33 AD, depending on calendar variations over the centuries