Read Romans 1:18 - 32
This section of Scripture tells us exactly what occurs in those who do not believe. It's not that they can't believe. It's that the unbeliever rejects the truth of God's Word when it is shared with them and the believer does not reject the truth when someone shares God's Word with them.
Romans 1:
18 For the wrath of God is revealed from heaven against all ungodliness and unrighteousness of men, who hold the truth in unrighteousness;
19 Because that which may be known of God is manifest in them; for God hath shewed it unto them.
Rom 1:18-19 tells us that the truth is suppressed when God makes it plain to them. The word "hold" in vs 18 is the Greek word katechō and it means to suppress; hold back; restrain. When the Word of God is spoken, it is restrained from reaching the heart of the unbeliever. They reject the truth. They reject God.
Because they suppress the truth, they do not glorify God, their thinking becomes empty and foolish and, as a result, their foolish hearts become darkened — Rom 1:20-21.
Because the heart is darkened, they profess themselves as wise but in reality they become fools and turn to idolatry — Rom 1:22-23.
Because of this, God gives them over to uncleanness — Rom 1:24.
Because they are given over to uncleanness, they degrade their own bodies and exchange the truth of God into a lie. They worship creation more than the Creator — Rom 1:25.
Because of this, God gives them over to vile affections — Rom 1:26.
Because they are given over to vile affections, they commit shameful acts and receive in themselves the adequate penalty for their error — Rom 1:27.
Because they do not like to retain God in their knowledge, God gives them over to a reprobate mind — Rom 1:28.
Because they have a reprobate mind, they exhibit all of the behaviors shown in Rom 1:29-32.
Look at how long God holds on to a person before he or she is given over to a reprobate mind. First it's suppress the truth; then the foolish heart becomes darkened; then given up to uncleanness; then given up to vile affections; then reprobate mind. Each time the person is given up to the next downward step, it is because he or she has rejected God.
These are the steps that are taken over the course of many years. God holds on as long as He can, but at some point, as they move further and further away from Him, God has to let them go.
It's not like they suppress the truth in unrighteousness one moment and the next moment they have a reprobate mind. There are more than several steps involved in the downward spiral to reprobate mind. And in the Greek the word reprobate means not standing the test; not approved.
And at any point, a person can allow the truth of God's Word to penetrate their heart and God will start working to bring increase to that little kernel of truth they do not restrain. God brings the increase in the heart of those who do not reject Him.