We are inexcusable
What does man know about God in his natural state? Man is created in God's image, and is given an eternal perspective to look beyond the routine of his daily life (Ecclesiastes 3:11). He knows about God's eternal power and divinity, through the realities around him of time, space, and objects. His sinful nature continually reacts against the evidence of God, and that is why man falls into idolatry, polytheism, agnosticism, etc. In his sin, apostate man "suppress the truth" and change the glory of the incorruptible God into an image: witness the diversity of world-religions, which, while they witness to man's religiosity, are a strong evidence of man's rebellion in worshipping a man-made god, a god made in human likeness.
At the very least, all humans have an inkling within themselves that there must be a supreme Being to whom they are accountable. But they invariably smother and quench, as far as they can, the awareness that this general revelation provides of the transcendent Judge and Creator. They do have an ineradicable sense of deity, but they transfer it to unworthy objects. However, God will not allow man to suppress entirely his sense of God and of His judgment. Some sense of right and wrong, plus the sense of accountability, always remain.
In his apologetic, "Basic Christianity", C.S.Lewis rightly starts from this fundamental point: every man, from all cultures and epochs, have a moral sense. When someone tries to cheat him, he cries out, "That's unfair." Whence did he get this moral sense? Even in the fallen world everyone is endowed with a conscience that from time to time condemns them, telling them that they ought to suffer for wrongs they have committed. Man will get rid of conscience if he can, for it bugs him constantly, but he cannot, for it is God's reminder to man that he is responsible and will ultimately give account. Man knows that God is a moral God, but he cannot know him as Saviour. They know that "he's there," but they hold this knowledge in guilt, with uncomfortable inklings of the judgment they cannot avoid.
How might this knowledge be used in evangelising? True evangelism has to start with the bad news first, as Paul did in Romans chapter 1-3. Only against the backdrop of man's rebellion and disobedience can the love of God and his gracious provision of redemption in Christ be appreciated. Luther used to emphasise the two aspects of the Law and the Gospel. The Law comes first. The Law makes the gospel both necessary and desirable.
In evangelising, the Christian may be assured that his contact knows already about God, though he has furnished himself with a thousand excuses and aberrations. But the link is there, and he can and should address him as a moral being, who stands condemned and guilty because he has not used aright the innate sense of God he has within himself.
Though the person may deny his moral obligation, yet the Christian must press him with the knowledge he already has. That's the starting point.
Other issues may be taken up later. For instance, since God exists and since God is a living God, then it is possible that God has spoken to us. Thus the Scripture, as special revelation, is brought in.