It is difficult to explain how someone 'cannot believe in God', when
all believe in God / devils believe in God / have no excuse Rom 1:20. It is easier to explain unbelief in Jesus.
1. Unbelief in Jesus = 1 Cor 12:3
Therefore I want you to know that no one who is speaking by the Spirit of God says, "Jesus be cursed," and no one can say, "Jesus is Lord," except by the Holy Spirit.
Making unbelief in Jesus = someone who rejects Jesus = failed the session of God's judgment Jer 17:10 / did not let Jesus in Rev 3:20.
2. Unbelief in God. Here is my stab at it

.... On the one hand we have Rom 1:20 that says all believe in God as all have seen evidence of Him all around them. But yet not all could say what Jonah did in Jonah 4:2
'I knew that thou art a gracious God, and merciful, slow to anger, and of great kindness, and repentest thee of the evil'.
Likewise Abraham would not have gone to the level he did in sacrificing his son... if he believed God was evil. It is because Abraham believed God was good, like Jonah. It is because Abraham believed in / had a revelation of who God actually is.
Making unbelief in God = someone who rejects God = failed a session of God's judgment Jer 17:10.
So when we preach about Jesus / good God we are preaching about a God they do not know. Following Rom 10:14. Which is good. But ...we cannot ignore that there is a reason they do not know. There is a reason we do know. The speaker is never technically us. God speaks through us. God reaches out to all mankind James 4:8. God uses us. Rom 10:14 is proof of that. God does not need us. Nobodies salvation is on our head.