Borne anew by the word of God
Chapter summary 1 Peter CHAP. I. Hee blesseth God for his manifold spirituall graces: 10 shewing that the saluation in Christ is no newes, but a thing prophesied of olde: 13 And exhorteth them accordingly to a godly conuersation, forasmuch as they are now borne anew by the word of God.
13 Wherefore gird vp the loynes of your minde, bee sober, and hope to the end, for the grace that is to bee brought vnto you at the reuelation of Iesus Christ:13 14 As obedient children, not fashioning your selues according to the former lusts, in your ignorance: 15 But as hee which hath called you is holy, so be ye holy in all maner of conuersation; 16 Because it is written, Be ye holy, for I am holy.16 17 And if ye call on the Father, who without respect of persons iudgeth according to euery mans worke, passe the time of your soiourning here in feare: 18 For as much as ye know that yee were not redeemed with corruptible things, as siluer and golde, from your vaine conuersation receiued by tradition from your fathers; 19 But with the precious blood of Christ, as of a Lambe without blemish and without spot, 20 Who verily was foreordeined before the foundation of the world, but was manifest in these last times for you. 21 Who by him do beleeue in God that raised him vp from the dead, and gaue him glorie, that your faith and hope might be in God. 22 Seeing yee haue purified your soules in obeying the truth through the Spirit, vnto vnfained loue of the brethren: see that ye loue one another with a pure heart feruently, 23 Being borne againe, not of corruptible seed, but of incorruptible, by the word of God which liueth and abideth for euer. 24 For all flesh is as grasse, and all the glory of man as the flowre of grasse: the grasse withereth, and the flowre thereof falleth away. 25 But the word of the Lord endureth for euer: & this is the word which by the Gospel is preached vnto you.
In the chapter summary we see "borne anew by the word of God". What is this word of God. Well we know that Jesus Christ has the name The Word of God (Revelation 19:13).
But it says  "this is the word which by the Gospel is preached vnto you". So we see that the word that Paul is talking about here is Pauls gospel.
So Pauls gospel is the gospel by which we are saved. But also notice that it says "this is the word which by the Gospel is preached vnto you". What is this word preached unto you. The word is The Word which is the Lord Jesus Christ. It is Jesus Christ that is preached unto you by the Gospel.
Before Pauls ministry, Jesus only came for the lost sheep of Israel
Matthew 15 22 And behold, a woman of Canaan came out of the same coasts, & cried vnto him, saying, Haue mercy on me, O Lord, thou sonne of Dauid, my daughter is grieuously vexed with a deuill. 23 But he answered her not a word. And his disciples came, and besought him, saying, Send her away, for she cryeth after vs. 24 But he answered, and said, I am not sent, but vnto the lost sheepe of the house of Israel.
So it was after Stephen was stoned that salvation went to the gentiles and Paul became the minister of the gospel to the gentiles.