Those who stubbornly refuse to believe, won’t believe as long as their hearts remain hard, no matter how much proof and evidence are presented to give them reason to believe. Therefore it would be useless to debate them unless they are truly interested in learning.
If they are interested in learning, however, they can start by researching the shroud of Turin, the tilma of Guadalupe, and the Eucharistic miracle of Lanciano. They can also consider the complexity of the universe and of the human body and how unlikely such things are to be accidents.
St Thomas Aquinas has some interesting things to say on the subject also, and then there’s the personal experience of myself and countless of other persons throughout human history. (Atheism only became a thing recently, remember, another proof in God’s favor.)
Personally, I think an atheist is just a believer who hides his belief, even from himself, out of fear or anger.
After all, it is a common move of the human psychology to convince itself of the nonexistence of a reality it finds unpleasant. People only believe what they want to believe. At the end of the day, though, God’s existence isn’t affected by belief or unbelief, He’s still there.
It would be a more profitable discussion to inquire of the particular atheist why he/she is an atheist and when it started. Perhaps a tragic childhood experience such as the loss of a parent and the question of “Why didn’t God answer my prayer for his/her healing?” left unanswered caused the individual to question God’s goodness and atheism was a subconscious solution to exact revenge on the One seen responsible for the tragedy. Or perhaps on seeing the obligations of religion in the lives of other people, the person in question was afraid of having to answer to God for fear of his/her life being burdened and no fun and atheism was the subconscious solution to being able to live a “free” life. Or again, perhaps the particular individual was simply raised that way in a very strictly atheist environment. Not only is it very hard psychologically to abandon the beliefs your parents or guardians have drilled into you all your life, but the consequences of believing differently could result in the rejection of loved ones or of peers looking down on the individual as “intellectually inferior”. Thus atheists are deserving of our compassion and would possibly be better served by a more therapeutic approach rather than mere intellectual debate.
We will each see the truth at the end of our lives. If atheism is correct, theists have nothing to worry about since their death will be without an afterlife anyway and therefore unaffected by their beliefs. If theism is correct, however, then the atheists who meet God face to face are gonna wish they had given Him a chance.
Amo Iesu by Grace Pax 