Ultimately, It's Faith
For someone who accepts the bible as the ultimate authority, there are persuasive arguments to help a person understand why the secular theories regarding evolution cannot be correct. However, for the person who does not consider the bible an authoritative source, the "best" result is quite different. If we can leave the unbeliever with two opposing theories, neither able to disprove the other, then have we not accomplished all that we are able?
We cannot argue anyone into belief, even with observable science. All we can do is show them the assumptions and inconsistencies in the secular view and pray that God opens their eyes to the truth of his Word and the saving work of Jesus on the cross.
Our purpose in speaking to an unbeliever should not be to convince them of young earth creationism, but to share the gospel with them. Of course, we can do that through a conversation about origins very easily. We must remember that our part is to give an answer of the hope within us; the Holy Spirit of God does the convincing.