"The word "Church" (Latin ecclesia, from the Greek ek-ka-lein, to "call out of") means a convocation or an assembly. It designates the assemblies of the people, usually for a religious purpose. Ekklesia is used frequently in the Greek Old Testament for the assembly of the Chosen People before God, above all for their assembly on Mount Sinai where Israel received the Law and was established by God as his holy people. By calling itself "Church," the first community of Christian believers recognized itself as heir to that assembly. In the Church, God is "calling together" his people from all the ends of the earth. the equivalent Greek term Kyriake, from which the English word Church and the German Kirche are derived, means "what belongs to the Lord."" -Catechism of the Catholic Church
I'm tired of hearing people say "happy birthday Church", the Church is much older than Pentecost. It's a dispensationalist error to say the Church was born on Pentecost.
The Trinitarian founding of the Church was in some way instituted by the Father in the election of Israel, some way instituted by Christ with his institution of the apostolic ministry, and some way instituted by the Holy Spirit at Pentecost.