Indeed it was Acts 2. The word "church" is clearly mentioned in Acts 2:47: Praising God, and having favour with all the people. And the Lord added to the church daily such as should be saved.
While this directly applies to the ekklesia or assembly at Jerusalem, it intimates the beginning of the Church (the Body of Christ) also -- those who had received the gift of the Holy Spirit, therefore the gift of eternal life.
While Christ mentioned the Church before it came into existence, the Church could not begin until the Holy Spirit was poured out from Heaven on the day of Pentecost. Since Pentecost was a harvest feast, it prefigured the harvest of souls on that day through the preaching of the Gospel.
Believing Israel is called "the good olive tree" so the Church began with saved Jews. Indeed the commandment of Christ was to preach the Gospel in a specific progression: Jerusalem, Judea, Samaria, and then the rest of the world (beginning with the Roman empire). But Gentiles were added very shortly thereafter.
However, the "mystery" of the Church was only revealed to Paul later on, since it has not been revealed to the OT prophets, and even to the other apostles. But the Church was already in existence since 30 AD.