Church is translated from the NT word ecclesia ... which means "called-out ones" ?
One could argue that the church began as Christ began collecting His disciples.
Or ... that it began at Pentecost when the Holy Spirit came upon those gathered in the upper room.
Paul says ... in 1 Corinthians 3. that the Church was founded upon Christ ...
10 According to the grace of God which was given to me, as a wise master builder I have laid the foundation, and another builds on it. But let each one take heed how he builds on it. 11 For no other foundation can anyone lay than that which is laid, which is Jesus Christ.
... and Paul teaches, in Ephesians 2 ...
19 Therefore you are no longer strangers and foreigners, but fellow citizens of the saints and members of God’s household,
20 built on the foundation of the apostles and prophets, with Christ Jesus Himself as the cornerstone.
21 In Him the whole building is fitted together and grows into a holy temple in the Lord.
22 And in Him you too are being built together into a dwelling place for God in His Spirit.