The separation from the Jewish leaders and synagogues was gradual, but when you use the term OT Jewish faith, the apostles saw themselves aa following the faith and the Jews who did not follow Christ as departing from it.
They believed theirs was the faith that fulfilled the Scriptures (see Appendix).
However, Peter saw Gentile Christianity separating from Judaism starting with his vision and continuing with proclaiming the gospel to Cornelius in Acts 10. Specifically that Christianity spread to the gentiles without them becoming Jewish proselytes. Many of the Apostles heard and accepted this when Peter explained his actions to the church in Acts 11.
We have no record of exactly when Paul realized this, but it was before the Jerusalem Counsel in Acts 15. Acts 5:15 doesn't clearly state this. In Acts 13 Paul turned to the Gentiles after first going and getting thrown out of the synagogue. The jealousy in the synagogue may well be Paul telling them about Peter's experience in Acts 10 and 11 as well as his conversion experience.
The Jerusalem Counsel in Acts 15 was the final settling on the fact that the Gentile Christians did not need keep the Law of Moses as Jewish proselytes. At this time it was clear as far as Gentile Christians being separate from Judaism.
Appendix: Scriptures Fulfilled Quotes from ESV
54 But how then should the Scriptures be fulfilled, that it must be so?”
56 But all this has taken place that the Scriptures of the prophets might be fulfilled.” Then all the disciples left him and fled.
49 Day after day I was with you in the temple teaching, and you did not seize me. But let the Scriptures be fulfilled.”
21 And he began to say to them, “Today this Scripture has been fulfilled in your hearing.”
37 For I tell you that this Scripture must be fulfilled in me: ‘And he was numbered with the transgressors.’ For what is written about me has its fulfillment.”
18 I am not speaking of all of you; I know whom I have chosen. But the Scripture will be fulfilled, ‘He who ate my bread has lifted his heel against me.’
12 While I was with them, I kept them in your name, which you have given me. I have guarded them, and not one of them has been lost except the son of destruction, that the Scripture might be fulfilled.
24 so they said to one another, “Let us not tear it, but cast lots for it to see whose it shall be.” This was to fulfill the Scripture which says,
“They divided my garments among them,
and for my clothing they cast lots.”
So the soldiers did these things,
The Death of Jesus
28 After this, Jesus, knowing that all was now finished, said (to fulfill the Scripture), “I thirst.”
36 For these things took place that the Scripture might be fulfilled: “Not one of his bones will be broken.”
16 “Brothers, the Scripture had to be fulfilled, which the Holy Spirit spoke beforehand by the mouth of David concerning Judas, who became a guide to those who arrested Jesus.
8 If you really fulfill the royal law according to the Scripture, “You shall love your neighbor as yourself,” you are doing well.
23 and the Scripture was fulfilled that says, “Abraham believed God, and it was counted to him as righteousness”—and he was called a friend of God.
The Holy Bible: English Standard Version. (2016). (Mt 26:54–Jas 2:23). Wheaton, IL: Crossway Bibles.