I felt like I was speaking to a brick wall. I would make a point regarding the existence of God, and the person I was speaking to would respond as though he had not heard a word I said. It was quite remarkable to see his mental/emotional wall block every single thing I said. He did not actually respond with anything that could be called a refutation, but mostly just a deflection of the subject at hand. He had already told me that he did not believe that God existed, so I knew I had a battle. Scripture, however, tells us that his claim is not true.
We are told in today's first Mass reading that God has revealed Himself sufficiently to everyone, such that there is no excuse for denying His existence (cf. Romans 1:19). This revelation is given within the heart of every human. No, He has not revealed enough to everyone for them to know the specifics of Catholic dogma (that takes special revelation which comes only through the Church), but if they know that He exists, then they are obligated to learn more about Him. Thus, while I was speaking to the man mentioned above who was denying the reality of God, I knew that down deep he was only trying to cover up something that he did not want to admit: God is real, and we are all accountable to Him for everything that we do.
Knowing that people already know God exists changes our perspective on evangelism. We are not speaking to people who are completely ignorant, we are instead speaking to people who really do know the truth; we know that they know, and yet they do not want us to know that they know. It should be obvious that there is a radical ignorance of the details of the Catholic faith. Yes, many pagans recognize what a rosary is, but few know how to use it. Furthermore, numerous people have never even heard the word "Eucharist" or even know the basics of what a Mass looks like.
When you couple together the innate knowledge of the existence of God with the common ignorance of the things of God, we have a wonderful situation. This means, for those of us who want to live out our faith and seek to evangelize the lost, people are "ripe for the harvest". They know God exists, but likely do not have a burden of errant views of Catholic theology. We can tell them what "Eucharist" means without having to refute errors. Certainly, there will be those protestants who have been told all the lies about Catholics worshipping both the Blessed Virgin, and statues (etc.), but evangelizing them is quite different from the average pagan; and pagans are increasing in number at a remarkable rate these days.
The so-called "nones" who proudly claim that their religious identity is "nothing" are needing to be dealt with. You likely know a few of them (even if you are not aware of it). Their ideology is "forget about God, all I care about is my own feelings and opinions" (something of a solipsism in disguise). The want to claim that they "do not know" if God exists (and likely say they do not care), but Saint Paul tells us differently, and that matters for us. We can approach them with the awareness that they are merely trying to suppress the truth in their sin (cf. Romans 1:18). Essentially, we do not need to "prove" God to them, but rather make them see that their denial is contrary to reality.
Live out your faith in this faithless age. Exemplify what it means to believe in the Triune Creator of all things. Know that down deep they know that you are correct, and that they must repent if they are going to find any true peace. Above all, speak to them of the wonderful saving grace of Christ. Help them to know of His love and mercy so that they can feel confident in approaching Him. This is what it means to evangelize.