Suljaković's singing career began after her mother moved the family to their grandparents' home in the Širokača neighborhood of Sarajevo. Their neighbor Sena was a folk singer married to an accordionist and performed at a local kafana frequently. One night, Sena persuaded Šemsa to come with her to the kafana. That night Šemsa discovered her talent for singing and the next day the owner of the kafana asked her to start singing there nightly. Her music career officially began in 1971.