Does the Holy Spirit convict every human being of their need for salvation through Jesus Christ; Or does the Holy Spirit only convict the elect of God (i.e. those who have accepted the work of the Holy Spirit)? Also, what happens to those who have not even heard of Christ? Is the Holy Spirit convicting them; or is it our duty to preach the Gospel of Christ to them first so the Holy Spirit may convict them?
One of the roles of the Holy Spirit is to lead unbelievers to the faith. The Holy Bible says, "no one can say that Jesus is Lord except by the Holy Spirit" (1 Cor 12:3). This happened to Cornelius the Gentile when God's Spirit worked in him and even gave him gifts and led him to faith. So, unless the Holy Spirit works in an unbeliever, he cannot attain faith. It is up to the individual to accept or to quench the Holy Spirit and His work.
I wonder if in our present time there is still anyone who has not yet heard of our Lord Jesus Christ; and if so, what is the percentage in relation to the world population and the number of Christians in the world? I believe that the percentage is really minimal. It is definitely our duty to go preach the gospel and evangelize. This was our Lord Jesus Christ's command to His disciples before ascending into the heavens "Go therefore and make disciples of all the nations, baptizing them in the name of the Father and of the Son and of the Holy Spirit, teaching them to observe all things that I have commanded you; and lo, I am with you always, even to the end of the age. Amen" (Mt 28:19-20). However, God has given every individual the free choice to accept or reject the Holy Spirit. The Spirit of the Lord moved the heart of Felix the governor who, on hearing St. Paul speak about righteousness, self-control and the judgment to come, became afraid; and instead of accepting the works of the Holy Spirit, he said to St. Paul "Go away for now; when I have a convenient time I will call for you" (Acts 24:25).