The Bible refers to the Holy Spirit as the Spirit of grace (Hebrews 10:29). Grace comes before our response to the gospel. The Spirit of grace initiates our conversion. The Spirit of grace brings salvation to all who believe the gospel of Christ.
Jesus paid every believer's sin debt in full (1 John 1:7). The risen Christ saves all who believe on Him (Acts 16:30-31). The Spirit of God gives the abiding gift of faith in Christ for our salvation (1 Corinthians 13:13).
The Holy Spirit convicts of the sin of unbelief. The Holy Spirit convicts us, pricks our hearts, and awakens us to our need for the Savior (John 16:7-11). The Spirit of grace prepares us to be saved through faith in Christ.
The gospel of grace is Christ crucified for our sins and risen from the dead (1 Corinthians 15:1-4). The Holy Spirit brings the gift of faith to trust in Christ. We receive faith by hearing the word of God, inspired by the Holy Spirit (2 Timothy 3:16). "So then faith comes by hearing, and hearing by the word of God" (Romans 10:17).
God our Father draws us to Christ, through the Spirit of grace (John 6:44). The Holy Spirit enables our response to the gospel of Christ (1 Corinthians 12:3). We respond to the gospel through the Spirit of grace, believing on the Lord Jesus Christ.