In the beginning, God...
Christian apologetics has its place, just not at the front of the line.
I write this, because there's a difference between sharing the Gospel and defending the Gospel.
A few years ago, someone gave me a copy of an evangelism program that advertises itself as a story approach. The program started in Genesis, though not with the actual story that Genesis tells. It began instead with a lesson on God's existence. The next lesson explained the nature of the Bible as the Word of God. The lesson after that focused on creation and set forth the nature of man as both a material and immaterial being. The lesson after that made a brief reference to the fall, before moving on to the theology of sin and death.
Somehow, in the author's mind, beginning the program in this way meant he was using a story approach.
But not so fast.
Instead of the story told in the Bible, the author was actually starting with an explanation and defense of Theology Proper, Bibliology, Anthropology, and Hamartiology. The chapter on the theology of God especially caught my attention in contrast to the way the Bible story begins—several pages of text to explain and defend what the Bible asserts in just four words (in English): "In the beginning, God..."
One reason not to begin Gospel proclamation with a theology lesson on God, or an apologetic for the existence of God, or for the Bible as the Word of God, or for creation vs. evolution, or for the nature of man, etc., is the likelihood of getting bogged down in argument before you're able to tell who Jesus is, and how he fits into God's plan to save us. Worse yet is not being able to tell about Jesus at all, because the person you're talking with refuses to agree with a theological proposition that you've asserted as pre-conditional to their believing in anything else you have to say.
Christian apologetics can play a profound role in persuading someone to believe in Jesus, but perhaps only after they have some idea of who Jesus is, according to the Bible's story about him. Even the Apostle Paul used a story-of-Jesus-first approach, and with an audience that was primed to argue apologetics. Acts 17:18 reports that Paul preached Jesus and the resurrection to his hearers in the synagogue at Athens. And when given the chance to go into more detail at the Areopagus, Paul doubled down on his approach, explaining that God "has fixed a day on which he will judge the world in righteousness by a man whom he has appointed; and of this he has given assurance to all by raising him from the dead."
In other words, Paul first made sure that his hearers knew who Jesus is, and that he had risen from the dead. Following this initial type of "argument" (a "defense" of who Jesus is), Paul's audience was primed to hear more of an apologetic for resurrection from the dead.
I know there can be exceptions to what I am advocating in this post. But I believe this to be something that generally holds true: When sharing the gospel with others, lead with the story of Jesus, utilizing the story-arc of the Bible from Genesis 1:1 going forward. Don't begin with a defense of the story, or of the theology of the story; just do what the Bible itself does. Tell it like the true story that it is. There will be many opportunities for apologetics to play its role from there.