The Church in New Testament was founded when the Holy Spirit filled the congregation in Jerusalem during the Pentecost.
The members of the congregation were filled with the power and were able to testify to people from other nations in their own languages.
Peter preached to the people gathered and declared that this was the fulfilment of the prophecy of Joel.
Peter also declared truths about Jesus Christ and 3000 people were saved that day because of his speech.
Church of Christ is formed by the people who believe in Jesus and confess Him as their Lord King and Savior in their lives.
In this sense, there only exists one Church of Christ, one giant congregation of all the people who believe in God.