With her early January birth date, Ban missed the eligibility cutoff for the 2001 World Championships by 11 days. She was forced to wait until 2002 to make her international senior debut. At the 2002 World Championships in Debrecen, Ban won a silver medal on the balance beam, one of Romania's only victories of the competition, and placed fourth on the floor finals. Later that year she placed second all around at the Chunichi Cup (behind teammate Oana Petrovschi) and won the Massilia Cup. In 2003, Ban had a similarly strong showing, contributing to the Romanian team's silver medal at the 2003 World Championships and placing sixth in the all-around final. That year she successfully competed in several international competitions, winning the all around silver medal at the Gander Memorial behind Cătălina Ponor and the all around bronze medal at the 2003 Chunichi cup behind Andreea Munteanu and Svetlana Khorkina. She also won silver on beam at the 2003 Cottbus Cup and the 2003 DTB Cup and won the Swiss cup together with Marian Drăgulescu.