Have you considered that those who are unregenerate already know God, but they know Him as an enemy, not as a friend. Romans 1 declares although they "knew God" they "suppressed the truth in unrighteousness". So they are guilty for rejecting what they KNOW. When they hear us preach the gospel they reject it outright and will not believe because they "love darkness" and "hate the light" (John 3:19). Then the truth that they know and hate is changed altogether by God to a truth that they know and loves. Before that time, unless God opened their eyes and ears, they could neither see nor hear (Deut 29:4, 30:6) because they would not. It is a matter of their love and hate, not a matter of simply having no conception whatsoever of what is being said. They understand the concepts being communicated well enough, they just hate it. How could they be "hostile to God" (Rom 8:7) if they knew nothing about Him?
So if the unregenerate cannot understand God, what is the use of declaring the gospel? When we proclaim the law (and gospel) to unbelievers we do not preach it thinking they will want it, or believe it on their own. No Paul says the purpose of the law is not to show their ability, but to reveal sin.(Rom. 3:19) But we do so always with an eye to God that the things we say will be used by God to convict them as He changes their heart of stone to a heart of flesh, so they will flee to Christ as their only hope. People are not saved in a void but through the gospel. James says, “He chose to give us birth through the word of truth” (James 1:18).
Part of a comment by Patrick Korseck I think will be helpful here:
We must remember that God does not merely appoint the ends, but also the means. The same logic of determinism used to condemn freedom of conscience can be used to discourage evangelism or even prayer, yet the Bible consistently teaches that we have creaturely agency in God's conduct and that the prayers of the righteous are effective. This does not lead to synergism but to the conclusion that these are the means appointed by God, in His ineffable wisdom and skill, for bringing about His appointed ends. We, as Christians, do not rely upon angels to evangelize. We do not passively test the Holy Spirit by leaving Him alone to regenerate the sinner. We acknowledge that God has placed His treasure in jars of clay and that the great commission is given in sincerely and earnestly to us. Paul says he becomes all thing to all men so that some might be saved. The Muslim relies upon political coercion. The deist retreats in fatalistic apathy. The Christian obeys the gospel by preparing himself to give an answer to anyone who asks about the hope within.
Consider this, though many miracles are recorded, God has decreed that His Word would be the means of calling men to Himself. What is God's Word if not persuasive? We who follow Christ are called blessed for believing without seeing, by relying upon His Word. Likewise we win others in the same manner.