I have asked my MCCC philosophy students (60-100 per semester), over a period of 15 years, the question: "How many of you have heard of Richard Dawkins?" One student in 30 has responded yes. A slightly larger percent say they used to be Christians but have become atheists. Maybe 2 or 3 out of 30 say this.
When my students are presented with logical, philosophical (and essentially non-religious) arguments for or against the existence of God, at least 50% say they are interested. Their interest is evident in the classroom discussions and interaction. A small percentage of my students, as a result of taking my classes, have converted from atheism to theism. (I estimate 5 out of 30 students do this; and probably slightly more.)
So I think students are interested in rational argumentation about God's existence. Virtually none of them have ever thought this way before.
For my students, as well as for humanity in general (and even myself), experience is more persuasive and needed than argument. Christian theists like myself should make a case for our beliefs. I do think God can encounter an irreligious person through sound argumentation. (Like, e.g., we see in Acts 17.) But experience is very, very powerful, and should not only not be relegated as veridically inferior to reason but as epistemologically essential. Experience, not theory, breeds conviction. (I think it is ultimately impossible and misleading to separate "reason" and "experience.")
Terry Eagelton, in Culture and the Death of God, writes:
"Hegel notes in the Phenomenology of Mind that the abiding concern of the Enlightenment is the battle against religion - although he also insists that since religious faith has in any case been reduced to propositional status, as a body of theoretical knowledge or science of the deity, it has grown every bit as impoverished as the rationalism which lays siege to it." (Eagelton, Culture and the Death of God, 4)
One reason (perhaps the reason) my students have never heard of Richard Dawkins or his worldview siblings is because his rationalism (so-called) is experientially vapid.
One reason some of my students have left Christianity (so they say, and well may have) is because their experience of "church" is as a head without a heart. Unless church captures people from the neck down we'll find more leaving. And, BTW, they'll eventually be leaving their newfound unbelief for the same reason. (Some, like Julian Barnes and John Gray (following Nietzsche, to Nietzsche's credit), have attempted to write about the experience of godlessness.)