Church today started at Pentacost ?

https://doctrine.org/the-church-the-body-of-christ
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The majority of Christians today believe the Church today started at Pentecost Acts 2:1-4 or Matt 16:18
Yet Paul taught that the Church today - The Body of Christ started much later.
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"Three major problems exist for the traditional view.
The first is God explicitly stated through the apostle Paul that the Church, the Body of Christ, was a “secret,” (μυστήριον).
This presents a serious problem for the traditional view because Paul made this declaration long after Pentecost.
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The second problem confirms the first point.
No Biblical evidence exists to support the view that anyone at Pentecost recognized that the Church, i.e., the Body of Christ, had come into existence.
On the contrary, the Scriptural evidence indicates at Pentecost the Twelve knew nothing about the Body of Christ.
Peter only addressed Jews.
But Paul declared the Church was that organism in which Jew and Gentile are equal.
Peter obviously did not know this else he would have addressed Gentiles.
Furthermore, only Paul wrote about the Body of Christ (Romans 12.5;1 Corinthians 10.16,17,12.12,13,18,25,27;Ephesians 1.23,2.16,3.6,4.4,12,16,5.30;Colossians 1.18,2.17,19,3.15).
Such terminology is absent from the Gospels and the letters of Peter, James, John, Jude.
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Lastly, Peter and the Eleven were looking for thefulfillment of prophecy, i.e., the kingdom of God on earth which God had revealed through the prophets, not the beginning of a new “Church” age.
The Old Testament contains not a word about the Church, the body of Christ.
The prophets, John, and Jesus had revealed nothing of the fact that Jew and Gentile would be equal in Christ in a Body.
On the contrary, Peter quoted Joel and expected the “sun to be turned into darkness and the moon into blood” (Acts 2.15-21).
Peter expected the Lord to come in judgment and to establish His kingdom.