If you are not aware of a moment when you asked Christ to come into your life as your Lord and Savior, you are not a Christian and never have been. You are just labeling yourself with a term that has no real significance or meaning in your life. Church is your social club. Unfortunately, I believe the majority of people who identify with Christianity are in just this tragic position.
It is impossible for a baby to be born a Christian. That's why, as Jesus himself said, you must be born again. Your birth into this world is a physical birth. To be a Christian you must be born spiritually, "...for all have sinned and fall short of the glory of God..." Romans 3:23
It is not possible to be a Christian on the basis of being born into a family of Christians. You cannot inherit Christianity. This is the difference between Christianity and all religions such as Islam, Buddhism, Hinduism, etc. Christianity is a personal relationship with God himself and, therefore, requires spiritual birth into the family of God.
John 3:3-7: Jesus answered and said to him, “Most assuredly, I say to you, unless one is born again, he cannot see the kingdom of God.” Nicodemus said to Him, “How can a man be born when he is old? Can he enter a second time into his mother’s womb and be born?” Jesus answered, “Most assuredly, I say to you, unless one is born of water and the Spirit, he cannot enter the kingdom of God. That which is born of the flesh is flesh, and that which is born of the Spirit is spirit. Do not marvel that I said to you, ‘You must be born again.’ The wind blows where it wishes, and you hear the sound of it, but cannot tell where it comes from and where it goes. So is everyone who is born of the Spirit.”
Having a personal relationship with Jesus Christ is initiated by your personal response to God's call, his tug at your spirit. It is a specific decision made at a specific time, out of a sincere heart full of repentence and belief that Jesus died on the cross for you. "For God so loved the world that He gave His only begotten Son, that whoever believes in Him should not perish but have everlasting life." John 3:16.
"Examine yourselves as to whether you are in the faith. Test yourselves. Do you not know yourselves, that Jesus Christ is in you?—unless indeed you are disqualified." 2 Cor. 13:5
How can you be sure that you have been born again? "The Spirit Himself bears witness with our spirit that we are children of God, and if children, then heirs—heirs of God and joint heirs with Christ." Romans 8:16,17
"Therefore, my beloved ... work out your own salvation with fear and trembling..." Phil. 2:12.