What period of time began when Paul started ministering the Gospel of Grace to the Gentiles?
That period is the Age of Grace, also called the Church Age. It began after Israel rejected her King and God raised up Paul to take the Gospel of Grace to the Gentiles. It is an undetermined period of unknown length, now over 1,900 years, ending when the Church is taken out so God resumes His prophetic program with Israel.
Les explains that when Israel would not believe and receive her King, God raised up another little Jew, the Apostle Paul, and first made known that He would send that man to the Gentiles. That opened the Age of Grace, the Church Age. Paul went immediately to the Jew, but then to the Gentile, and from the time Paul began ministering to the Gentiles with the Gospel of Grace there is an undetermined period of time. No one knows how long it will last, only that it has now come over 1,900 years. Then the Church must be taken out of the way so God can pick up where He left off with Israel, because that belongs back in the prophetic program. After the Tribulation, Christ will return and set up His Kingdom. Les also notes Paul did most of his ministry among the Gentiles and established churches from about A.D. 40 until he became a prisoner in Rome about 65, and from about 58–59 he began writing letters because the churches needed doctrine, correction, and instruction, with the Holy Spirit prompting him.