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The New Testament revelation about the coming of the person of Christ begins with the gospel accounts of his birth, life, death, resurrection, and ascension. However, the formation of the church and the church age did not begin until Acts 2 with the coming of the Holy Spirit when He began to indwelling all believers, forming the body of Christ—the church—by baptizing all believers into Christ (cf Acts 1:5; 2; 10:44-48; 11:15-18; 1 Cor. 12:12-13). In Acts 11:15f, Peter equates the Lord’s promise of Acts 1:5 with the coming of the Spirit in Acts 2. Further, 1 Corinthians 12:13 shows us that the baptizing work of the Holy Spirit is that which joins us into the body of Christ, the church. It is at this point that the church began and consists of both Jew and Gentile in one new man. This was a truth that was unrevealed in the Old Testament (see Col. 1:25-29).
From the standpoint of the dispensations or the various economies by which God governs the world, the Old Testament economy actually continued through the gospels. Acts is a transitional book moving from the Old Testament economy into that of the church age, the body of Christ. However, Christ was the fulfillment of the Old Testament promises—at least those that dealt with His first advent. With His death, Christ brought an end to the Old Testament covenant as seen in the tabernacle/temple, the sacrifices, and the Aaronic priesthood. It was for this reason that the veil of the temple was torn in two (Matt. 27:51). Hebrews gives further witness to this fact as did the institution of the Lord’s supper when He also observed what was in reality the last legitimate Passover because that very evening He would be arrested and die the next day as our Passover Lamb Himself (1 Cor. 5:7).
Thus, Acts was not the beginning of the New Testament, but it records the beginning of the church as the body of Christ. The gospels also contain much information that is pertinent to the church as the body of Christ as with John 13-17.