The answer
The Holy Spirit works in the unbelievers to make them believe.
Or how can they believe without the work of the Holy Spirit in them? Does not the Holy Bible say, "No one can say that Jesus is Lord except by the Holy Spirit" (1 Cor 12:3).
The work of the Holy Spirit to make people believe differs from His permanent dwelling in a believer.
The Holy Spirit may work in the heart of an unbeliever to call him to believe, or work a miracle or some wonder to him which might lead him to believe, but after believing, a person must obtain the Holy Spirit through the Holy anointment in the sacrament of the Holy Myron (Chrism) so that the Spirit may always work in him.
The Spirit may also work in the unbelievers for the benefit of the church.
As the Scriptures say, "The Lord stirred up the spirit of Cyrus, King of Persia. (Ezra 1:1). This was for the purpose of building the house of the Lord in Jerusalem. There are many similar events both in Scriptures and in history.
Thrice-Blessed Pope Shenouda III of Blessed Memory