Unbelief is an active work, not the absence of belief. You will not find the word nonbeliever or nonbelief in the scriptures. Unbelief is a willful posture of resisting God. Man may, in his own strength, resist God.
This includes denying what he sees in the natural world. The laws of creation (its existence, expanse, synergy, etc.) can be perceived by the natural man and the natural man's senses. From this, natural man should deduce that God is real. Even unrighteous men are given this proof. This is what Paul wrote about in Romans:
"For the wrath of God is revealed from heaven against all ungodliness and unrighteousness of men, who suppress the truth in unrighteousness..."
Here: an active work of unbelief: suppressing the truth. Paul goes on to explain that the witness of God is even in their very being:
"..because what may be known of God is manifest in them, for God has shown it to them."
Creation even testifies to the invisible traits of God, so all men are without excuse...
"For since the creation of the world His invisible attributes are clearly seen, being understood by the things that are made, even His eternal power and Godhead, so that they are without excuse."
These are not men who did not know God. They knew God through the testimony of creation. But they willfully unbelieved, and did not glorify God glory.
"..because, although they knew God, they did not glorify Him as God, nor were thankful, but became futile in their thoughts, and their foolish hearts were darkened."
Unbelief is the willful posture of resisting God: His testimony in creation and His testimony by the Spirit. Like it is written of the Jews here:
“You stiff-necked and uncircumcised in heart and ears! You always resist the Holy Spirit; as your fathers did, so do you."
But, unbelieving Jews can be grafted back into Christ if they cease to unbelieve.
"And they also, if they do not continue in unbelief, will be grafted in, for God is able to graft them in again."