It is virtually impossible to wake someone up who is feigning sleep. It is also futile to attempt to convince the natural man of the existence of God because He already knows that God exists by virtue of being created in God's image. Romans 1:19-21 states:
"For what can be known about God is plain to them, because God has shown it to them. For his invisible attributes, namely, his eternal power and divine nature, have been clearly perceived, ever since the creation of the world, in the things that have been made. So they are without excuse. For although they knew God, they did not honor him as God or give thanks to him, but they became futile in their thinking, and their foolish hearts were darkened."
While classical apologetics has sought to wake up the already awake, covenantal apologetics realizes that man's problem before God is not intellectual/epistemological but moral/covenantal. The natural man denies God's existence, not because of a lack of proof, but because of the desire to live autonomously, apart from the rule of God and creaturely dependence on Him. The love of sin and the love of God are mutually exclusive, and up until the Holy Spirit regenerates the sin-hardened heart in order that, through repentance and faith in Christ, man might be in the favorable side of the covenant, man will never wake up from his fake slumber.
Evangelism and apologetics stand in perichoresis to each other, and the way to engage the unregenerate is as follows:
"Here then are the facts, or some of the main facts that the Reformed apologist presents to the natural man. There is first the fact of God's self-contained existence. Second, the fact of creation in general and of man as made in God's image in particular. Third, there is the fact of the comprehensive plan and providence of God with respect to all that takes place in the universe. Then there is the fact of the fall of man and his subsequent sin. It is in relation to these facts, and only in relation to these facts, that the other facts pertaining to the redemptive work of Christ are what they are. Their very factness as facts would not be what it is unless the facts just mentioned are what they are." (Cornelius Van Til, Christian Apologetics [New Jersey: P & R, 2003], ed. William Edgar, 193)
More on covenantal apologetics here.