I don't think you'll do something competent. Few people are gnostic-atheist. Most people are agnostic-atheist or agnostic-theist.
But even if showing rational arguments for God somehow convinces somebody, it will not change their world. It's not like reality is going to drastically change the moment they accept God exists.
But even if acknowledging the existence of God makes them want to learn more, what do they do? They could lean toward Deism, they could lean toward some spiritual-but-not-religious garbage, they could lean toward Islam, they could lean toward Christianity. And if Christianity, then which form? Catholics and Orthodox mutually anathematize each other, and Protestants can range from being as much of a secret club as Catholicism, to being all lovey-dovey about how we're all siblings in Christ.
So you have to: give convincing arguments for theism, give convincing arguments for Christianity, give convincing arguments for the particular tradition you believe is true, and hope that the person reading doesn't misinterpret your point, or doesn't quit after any one of the steps to do their own thing afterward.
This may just be because of my personal experience, but convincing people of the Church's origins (that Christ existed, that He was crucified, that the apostles and the early Church's behavior could only be explained by His resurrection) and giving them incentive to go to church to see what it's all about would be more productive, I think.