Howbeit when he, the Spirit of truth, is come, he will guide you into all truth. John 16:13.
The first work of the Holy Spirit is found in John 16:7-9. "Nevertheless I tell you the truth; It is expedient for you that I go away: for if I go not away, the Comforter will not come unto you; but if I depart, I will send him unto you. And when he is come, he will reprove the world of sin [He will convict or convince the world of sin], and of righteousness, and of judgment: of sin, because they believe not on me." Please underscore the Bible definition of sin given here. Sin is something more than doing wrong things--transgressions. The real issue is to not believe and trust in the Lord Jesus Christ. And the Holy Spirit has this reminder as His first work.
His first work involves the entire world. No one is left out. The poor heathen in some far-flung country is convinced of sin even before the missionary comes. The Holy Spirit has been there first. It is His work to convince the world of sin. Not one person is passed by. While you and I are sleeping, the Holy Spirit is somewhere doing His work of conviction.
If all there is to salvation is to be convicted of sin, everyone would be saved. But there is something further in the work of the Holy Spirit, and that is His second work, found in John 3:3-5. "Jesus answered and said unto him, Verily, verily, I say unto thee, Except a man be born again, he cannot see the kingdom of God. Nicodemus saith unto him, How can a man be born when he is old?...Jesus answered,...Except a man be born of water and of the Spirit, he cannot enter into the kingdom of God." To be born again is to be born of the Spirit. The second phase of the Holy Spirit's work is His regenerating work, which takes place only in the hearts and lives of the people who respond to it. In order for everyone to be saved, all would have to respond to the Holy Spirit's second work. Here's where the big difference lies.
The Bible makes it clear that God wants everyone to be saved but that only those who respond to His invitation can receive the new birth that is the potential for each one. As we choose today to accept anew the work of the Holy Spirit in our lives, He will do His converting work. As we respond to Him, we will be brought into harmony with God.