On page 2531 of the ESVSB in the article entitled “Biblical Doctrine: An Overview” under the subheading of “salvation” it reads as follows:
From God’s vantage point salvation begins with his election of individuals, which is his determination beforehand that his saving purpose will be accomplished in them (John 6:37–39, 44, 64–66; 8:47; 10:26; 15:16; Acts 13:48; 16:14; Romans 9; 1 John 4:19; 5:1). God then in due course brings people to himself by calling them to faith in Christ (Rom. 8:30; 1 Cor. 1:9; 2 Tim. 1:9; 1 Pet. 2:9).
God’s calling produces regeneration, which is the miraculous work of the Holy Spirit in which a spiritually dead person is made alive in Christ (Ezek. 11:19–20; Matt. 19:28; John 3:3, 5, 7; Titus 3:5). The revived heart repents and trusts Christ in saving faith as the only source of justification.
Notice that the editors clearly affirm that a regenerated, revived heart precedes repentance and trust in Christ. It goes on to describe saving faith as follows:
To be a Christian means one has traded in his “polluted garment” of self-righteousness for the perfect righteousness of Christ (Phil. 3:8–9; cf. Isa. 64:6). He has ceased striving and now rests in the finished work of Christ—no longer depending on personal accomplishments, religious pedigree, or good works for God’s approval, but only on what Christ has accomplished on his behalf (Phil. 2:8–9). A Christian understands with Paul that “it is no longer I who live, but Christ who lives in me. And the life I now live in the flesh I live by faith in the Son of God, who loved me and gave himself for me” (Gal. 2:20). As regards Jesus paying the penalty for our sins, the Christian believes that when Jesus said, “it is finished” (John 19:30), it really was. Because of this, “there is therefore now no condemnation for those who are in Christ Jesus” (Rom. 8:1), and they have been “saved to the uttermost” (Heb. 7:25). A miraculous transformation has taken place in which the believer has “passed from death to life” (John 5:24). The Holy Spirit empowers the transformation from rebellious sinner to humble worshiper, leading to “confidence for the day of judgment” (1 John 4:17).
Now moving away from the theological essays, we would like to point to some related commentary the ESVSB makes on a few important texts of Scripture which speak of regeneration: check them out here