I think you have misunderstood or have strayed off topic. IMO, the Spirit has not much to with it. The topic is: When did the church begin, and if you consider Tom's OP he is considering the word "church" more in a local sense.
Historically every denomination, both Catholic and Protestant have used water baptism as the door to the local church. When we baptize a person they become a member of our church. We wouldn't baptize them otherwise. It is a door to the church. It is a door to "our local church body or assembly. It is not the Spirit but water baptism. The only people we would baptize are those that are born again, willing to be baptized and in agreement with us in doctrine.
The word "church" is ekkesia, or assembly. That is all the word means--assembly.
Tom puts forth the idea, what is to prevent Christ and the Twelve from being called "the first assembly" of believers, or church. There is no specific doctrine that mandates the "coming of the Spirit." Here is an "assembly" of believers, Christ the chief cornerstone, and the apostles the foundation, with Christ saying "Upon this Rock (presumably Peter's testimony or Himself), I will build my church or assembly). There is no emphasis on the Spirit and doesn't have to be. Who makes that a requirement and why? It isn't in the definition of a local church, not any of the definitions that I have read.
Here is one of them:
A church is an assembly of baptized (immersed) believers who have voluntarily associated themselves together for the purpose of carrying out the two ordinances (Lord's Supper and baptism by immersion), and for obeying the Great Commission of our Lord.
That is what our church does.
As Tom pointed out, Jesus and his disciples did the same before the cross.
the Baptism of the Spirit gets one into the Church/Body of Christ, water baptism entry way for local church membership...