While training with Bud McAlister at CLASS Aquatics in her hometown of Northridge, Quance was selected to make her international debut at the 1991 Pan Pacific Swimming Championships in Edmonton, Canada, where she won gold and silver in the 200-meter breaststroke and 400-meter individual medley respectively. 1992 was a disappointment for Quance, as she missed selection for the 1992 Summer Olympics in Barcelona, Spain. She made a strong comeback at the 1993 Pan Pacs in Kobe, Japan, winning gold and bronze in the 400-meter individual medley and 200-meter breaststroke respectively. 1994 yielded her first medal at the global level, winning a bronze in the 400-meter individual medley and finishing sixth in the 200-meter breaststroke at the 1994 World Aquatics Championships in Rome, Italy.