I realize there are people in this world who deny God's existence and what I think about that is this: I think there are people who will say they have no belief in God and yet they do continue to have thoughts and feelings which conflict with their statements. The beautiful thing about this is that there is still an open space and God is trying to bring light in through that direction. He is trying to bring understanding to this person. Despite their general disregard of Him, God hasn't given up on them. On the other hand there are those who deny God's existence completely and have walked a very long way in the opposite direction and have become so unreachable that they don't experience those times of conflict regarding what they believe - for them, the possibility doesn't exist - and the roof hasn't fallen in on them and they are satisfied with life. They may feel life is as good as they had ever wished it to be. The thing to understand is that the fact of their total comfort in the situation does not bode well. It could be that a definite separation has occurred and God is not going to intervene in any way. They don't feel drawn because the reality is that the choice they have made has left them standing totally outside of God's presence. If there were any chance for them to respond to the invitation, that chance is probably almost nonexistent if God's spirit has drawn away. (which is why we should remember to pray for them, that this will change)
There is no way possible for any one of us to comprehend the things of God unless God himself reveals those things to us. Now, God freely gives that gift of understanding to each of us when we ask. God is spirit, and therefore the things we understand about God come to our mind through the spirit. It's a knowledge He imparts. When we come to Christ we receive God's spirit and the Bible tells us that His spirit works within our own spirit, and therefore we should no longer live our lives guided by the prior which was a life lived outside of this understanding. The Bible tells us that our flesh "wars against the things of God." God's answer to that is draw close to Him and He will bring us to that place where we have His direction to such a point that we are taken beyond, far beyond a mere existence in this world wherein we hope for better in a mortal body. He takes us to the spiritual place of our existence, in this life, when we follow His lead, and that is the leading of His Holy Spirit. And believe me, this is just a foretaste of the eternal, because the spirit never dies, and God's love never ends. It goes on and on.
For the atheist, the non-believer, the one caught somewhere in the middle: they can never put a stop to God's love and compassion for them. Nothing they will ever do will change the fact that they were born with a need within their own spirit for His love. They've not recognized it; they've not connected with it, but it is there inside of them. But does God strive with someone forever who has gone the way of total denial of His existence? Possibly not. God wants us to have the choice. It makes me think of the words from Old Testament scripture: "Oh that you would choose life!"