Yes, of course it's possible for a convinced atheist to become a believer—if they aren't close-minded. Unfortunately, in my experience many convinced atheists don't have an open mind, and aren't really willing to reexamine the evidence honestly and fairly. I hope that won't be the case with you.
I could, of course, give you a number of reasons why it makes sense to believe in God; you probably already know them. But the most important thing I can do is urge you to look at Jesus Christ—not through the "lens" of your past experiences, but through the "lens" of the New Testament. Before you begin reading it, I challenge you to pray something like this: "God, I don't even know if You exist—but if You do, show Yourself to me." God will answer that prayer.
Why do I urge you to look at Christ? The reason is because He made a very startling claim about Himself: He said He was God in human flesh. "I and the Father are one" (John 10:30). Do you want to know what God is like? Look at Jesus, "For in Christ all the fullness of the Deity lives in bodily form" (Colossians 2:9).
Jesus said, "Ask and it will be given to you; seek and you will find" (Matthew 7:7). Don't let anything keep you from seeking God, for He loves you, and coming to know Him will be the greatest discovery you will ever make.