Let us look at what happened at the time of Pentecost. Peter realized that in order for the prophecies of Joel which he quoted (Acts 2:16) to continue to be fulfilled then the nation of Israel had to repent and be converted, as witnessed by his words here:
"Repent ye therefore, and be converted, that your sins may be blotted out, that the times of refreshing shall come from the presence of the Lord; And he shall send Jesus Christ, which before was preached unto you: Whom the heaven must receive until the times of restitution of all things, which God hath spoken by the mouth of all his holy prophets since the world began" (Acts 3:21).
Israel did not repent and her opposition to the disciples of the Lord Jesus reached a climax at the stoning of Steven at Acts 7. In
The Berean Searchlight Win Johnson wrote:
"Matthew 12:31,32 states: 'Wherefore I say unto you, all manner of sin and blasphemy shall be forgiven unto men: but the blasphemy against the Holy Ghost shall not be forgiven unto men. And whosoever speaketh a word against the Son of Man, it shall be forgiven him: but whosoever speaketh against the Holy Ghost, it shall not be forgiven him, neither in this world [age], neither in the world to come.'
"These words of warning came from the lips of the Son of God while He walked among men in His earthly ministry. They were addressed to the religious leaders of the nation Israel. Their blasphemy against Him even when He hung on the Cross was forgiven by the Father in answer to the prayer, 'Father forgive them, for they know not what they do' (Luke 23:34).
"But when at Pentecost, Peter, filled with the Holy Spirit, announced the return of Messiah on the condition of Israel's national repentance, these leaders instigated a persecution that reached its climax in the stoning of Stephen, a godly man, 'full of the Holy Ghost' (Acts 7:54-60). It was here that the 'unpardonable sin' was committed by Israel's leaders. The Third Person of the Trinity had been blasphemed and His pleadings through the Apostles ignored. This sin will never be forgiven" (Win Johnson, "The Unpardonable Sin," The Berean Searchlight, Feb.2001, p.6).
The "unpardonable sin" was committed at Acts 7, and I believe that at that point in time national Israel was temporarily set aside. I believe that at that time the Holy Spirit baptized all believers into the Church, which is His Body. Shortly afterward Paul was converted and made the Apostle of the Gentiles.
At least that is the way that I see the transition.