When were the nuclei of the first churches formed?
The first Christian churches were formed after Jesus returned to life and ascended back up to heaven.
The first Christian church was located in Jerusalem. It began immediately after Jesus returned to heaven.
And as they were gazing intently into the sky while He was going, behold, two men in white clothing stood beside them. They . . . said, “Men of Galilee, why do you stand looking into the sky? This Jesus, who has been taken up from you into heaven, will come in just the same way as you have watched Him go into heaven.” Then they returned to Jerusalem from the mount called Olivet, which is near Jerusalem, a Sabbath day’s journey away. (NASB) Acts 1:10-12
The apostles remained in Jerusalem and on the first day of Pentecost, a week long Jewish feast, God started the church. The Holy Spirit came and empowered the apostle Peter’s sermon. The people believed what Peter told them about Jesus (v. 44), were convicted of their sin of rejecting Jesus (v. 37), and asked, “What shall we do?” How many people responded?
Now when they heard this, they were pierced to the heart, and said to Peter and the rest of the apostles, “Brethren, what shall we do?” Peter said to them, “Repent, and each of you be baptized in the name of Jesus Christ for the forgiveness of your sins; and you will receive the gift of the Holy Spirit . . . So then, those who had received his word were baptized; and that day there were added about three thousand souls. They were continually devoting themselves to the apostles’ teaching and to fellowship, to the breaking of bread and to prayer. Everyone kept feeling a sense of awe; and many wonders and signs were taking place through the apostles. And all those who had believed were together and had all things in common . . . (NASB) Acts 2:37-38, 41-44
This was the start of the church.
From there the wonderful news about Jesus started spreading to many cities. The truth about Jesus was then preached in the cities of Samaria (Acts 8:5-15), Damascus (Acts 9:1-19), Joppa (Acts 9:1-43), and Antioch. (Acts 11:25-27). The news about Jesus Christ continued to spread up into Greece and then into Italy. We know that it spread into Egypt and Africa (Acts 8:26-39).
The Christian church in Jerusalem was the center of the Christian faith. It was there that the apostles were first located. The church had elders with James, Jesus’ brother, being the lead elder of the church (Acts 15:3-23). From there the truth about Jesus spread and God caused the Christian church to grow.
So then, those who had received his word were baptized; and that day there were added about three thousand souls. (NASB) Acts 2:41
But many of those who had heard the message believed; and the number of the men came to be about five thousand. (NASB) Acts 4:4
And all the more believers in the Lord, multitudes of men and women, were constantly added to their number, to such an extent that they even carried the sick out into the streets and laid them on cots and pallets, so that when Peter came by at least his shadow might fall on any one of them. (NASB) Acts 5:14-15
This all started shortly after Jesus’ death, return to life, and ascension up into heaven in A.D. 33.
Reference Links:God's Design For The Church
Recovering the Pattern of Biblical Leadership
Jesus' Approach To Ministry