When did the Church Age begin?
Scripture teaches that the Church Age began on the Day of Pentecost, when the Holy Spirit was poured out on the believers gathered in the upper room and the Church was established.
The Church Age began on the Day of Pentecost. When the Holy Ghost fell upon the one hundred and twenty believers gathered together, Peter stood and explained what was happening by quoting the prophet Joel: "it shall come to pass in the last days, saith God, I will pour out of my Spirit upon all flesh." This outpouring marked the start of what Scripture calls "the last days," and that period began right there at Pentecost, not at some far future point.
From that day forward the Spirit was poured out on sons and daughters, young and old, servants and handmaidens alike, and this outpouring has continued throughout church history. This is described as the beginning of a dispensation, the fullness of time, in which the Church is gathered together in Christ. This dispensation is the Church Age, and it will come to an end when the Church is taken out.
The early chapters of Acts show what this new Church looked like once it was established at Pentecost. The believers continued steadfastly in the apostles doctrine and fellowship, in breaking of bread, and in prayers, and a great fear came upon every soul as wonders and signs were done among them. This was the culture that God established in His people from the very start of the Church Age, and it set the pattern for the Body of Christ that followed.
The scriptures
But this is that which was spoken by the prophet Joel; And it shall come to pass in the last days, saith God, I will pour out of my Spirit upon all flesh: and your sons and your daughters shall prophesy, and your young men shall see visions, and your old men shall dream dreams: And on my servants and on my handmaidens I will pour out in those days of my Spirit; and they shall prophesy: And I will shew wonders in heaven above, and signs in the earth beneath; blood, and fire, and vapour of smoke: The sun shall be turned into darkness, and the moon into blood, before that great and notable day of the Lord come: And it shall come to pass, that whosoever shall call on the name of the Lord shall be saved.
And they continued stedfastly in the apostles’ doctrine and fellowship, and in breaking of bread, and in prayers. And fear came upon every soul: and many wonders and signs were done by the apostles. And all that believed were together, and had all things common; And sold their possessions and goods, and parted them to all men, as every man had need. And they, continuing daily with one accord in the temple, and breaking bread from house to house, did eat their meat with gladness and singleness of heart, Praising God, and having favour with all the people. And the Lord added to the church daily such as should be saved.
That in the dispensation of the fulness of times he might gather together in one all things in Christ, both which are in heaven, and which are on earth; even in him:
From the books
This answer is drawn from these passages in the Mary Banks Faith Library.