Koné was born in Abidjan. Like many other Ivorian stars, he began his career at the famed youth academy at ASEC Mimosas, run by Frenchman Jean-Marc Guillou in his home country. Guillou recalls: "One day, when I was passing through his district, some kids stopped me. They kept saying, 'We've got Pelé living here, you've got to take a look at him'. Then, Koné came along. He was slightly built but I never doubted for one moment that he was a real find. I took him into the academy after a trial of just ten minutes, but I did tell him that the Pelé nickname would have to go. That's when he became Baky, and I think it's better that way."