"If ye have heard of the DISPENSATION OF THE GRACE OF GOD which is GIVEN ME TO YOU-WARD: how that BY REVELATION HE MADE KNOWN UNTO ME, THE MYSTERY..." Eph. 3:2,3,5,6,9. The age of grace began with Paul, when God revealed it unto him. Paul wasn't saved until Acts 9, so it could not have begun before then.
As to Peter and Cornelius..Acts 10. Just after the conversion of Saul in Acts 9..Peter hesitated to go to the Gentile Cornelius. Even after his dream, he doubted in himself what the dream meant..Even when he got to Cornelius Peter was still talking about it being "unlawful for a Jew to keep company, or come unto one of another nation"...(Acts 10:28).
Now we know that Christ sent the Apostles to spread the gospel to all nations, beginning at Jerusalem. So why did Peter hesitate to go to Cornelius? "Beginning at Jerusalem" is the key. Peter knew that FIRST the Nation Israel had to repent and accept Christ as Messiah before the gospel was carried to the other nations (Gentiles).
Peter was NOT out of the will of God when he hesitated to go to the Gentiles. He well knew the prophetic program, that the nations were to be blessed throught the RISE and SALVATION of Israel (Isa. 60:1-3). He was filled with the Holy Spirit, and he knew that God had raised up His Son Jesus to bless Israel first, in turning them away from their iniquities, so that the Abrahamic Covenant might be fulfilled. And THEN the nations might be blessed through them. Israel must FIRST be brought to Messiah's feet.
But in Acts 10, Peter was sent by a SPECIAL COMMISSION to go to the Gentile house of Cornelius, "NOTHING DOUBTING." The others at Jerusalem later called him to account for this action, but after he had "REHEARSED THE MATTER FROM THE BEGINNING, and expounded it by order unto them" they, in turn, "glorified God, saying, Then hath God also to the Gentiles granted repentance unto life". Acts 11:4,18.
When Peter went to Cornelius' household it was NOT according to the prophetic program or the so-called great commission. He was NOT sent to these Gentiles because Israel had received Christ, but in spite of the FACT that Israel, as a nation, was REJECTING Christ. But what Peter had done on earth was bound in heaven and Paul's subsequent ministry was later recognized and endorsed by the Jerusalem church ON THE BASIS OF PETER'S ACTION TO CORNELIUS. Acts 15:1-18.
See the wonderful time line here? Paul is saved in Acts 9. He does NOT go directly to Jerusalem to confer with the 12, but Christ sends him into Arabia. Acts 10 shows God showing Peter to go to Cornelius. You can see the change in dispensations taking place here. From Law to Grace. From Israel first, to Israel in continuing unbelief, and God making this one step to Cornelius the proof to the 12 that Paul's revelations from the risen Christ and his commission to the Gentiles if TRULY FROM GOD.
Remember, before Peter was commanded by God to go to Cornelius, Paul, the Apostle to the Gentiles, had ALREADY BEEN SAVED and given his commission. Although the 12 were not aware of this yet, the story of Cornelius will come back to prove Paul's authority and commission as the Apostle to the Uncircumcision.
Just remember that Acts is a transition Book. From Law to Grace, from a Kingdom of believers to a Body of believers.