We don't get the Holy Spirit to enter us. He's God. He's not on a string. John 3:5-9 tells us that the Spirit goes where the Spirit desires. Not where we desire. He's like the wind. It blows where ever it pleases.
There would be no reason to hold people responsible for believing or failing to believe in Jesus if the unregenerate person cannot actually believe. If God is the one who imparts faith to the unbeliever, then the responsibility to believe lies not with man but with God, and therefore, God can have no basis on which to judge people for failing to believe.
If faith is a gift, then many commands in Scripture that exhort, command, prompt, and warn believers to live obediently become superfluous because the ultimate end of infused faith guarantees the sanctification of believers without their involvement (Lopez, “Is Faith a Gift From God?” 275).
So for biblical, theological, and practical reasons, we conclude that faith is not automatic, nor is faith a gift from God.
Faith comes through hearing the Word of God, through the convicting and drawing work of the Holy Spirit, and through responding to the revelation that one has already received from God.
Original Sin, from the fall, puts all humans into a situation whereby they can't believe. That's Church Teaching. It's Catholic, its Orthodox, It's protestant. It however is not cultish. It is not humanity's point of view. Certainly none of the other religions believe man can't believe. It is a uniquely Christian idea. I'm not even sure the Jews teach it, although their prophets surely did.
The Catholic church and the Orthodox church deal with it differently than the Protestant Church. They see baptism as the means of dealing with original sin. The non-Reformed protestant church deals with it by way of what they refer to as Prevenient Grace. Some even deny original sin as a concept. (I don't call consider them true protestant churches since they deny the fall.) The Reformed churches tend towards the doctrines of grace. We say faith is a gift since Paul calls it so. We deny the idea of prevenient grace since it is so vague. We don't think water baptism saves, although it is a sign of the covenant and brings people into covenant with God. And as such we believe it is a command of God to baptise, infants within the faith and adults who convert.
The Reformed churches also hold to the view that God is sovereign. Salvation belongs to him. And he will save whom he will save. He will have mercy upon whom he will have mercy. Go and read Romans 9 - it's a helpful read.
God elects whom he will save. He does it according to his own holy will. He has also created some for his holy wrath. Romans 9:22-23 We say - we believe because we are saved. Not that we are saved because we believe. We read John 3:16 as a declaration of the gospel. It's a warning. Not an invitation.
We say that God's rules of ethics and morals and justice belong to him, and not the same as humanity. God is never and can never be held to a human account.