Korpi began skating at the age of five, following her older sister. She landed her first triple jump, a salchow, when she was 11 or 12.
Korpi enjoyed some success as a junior skater, twice winning the junior national title and medalling at three junior Grand Prix events, including a gold in 2004. She won the silver medal at the 2005 Finnish Nationals, qualifying her for the 2005 European Championships, where she placed 13th; she then competed at the 2005 World Junior Championships, where she came in tenth, her best finish at the event.
The following season, Korpi remained on the ISU Junior Grand Prix, but placed 3rd at the 2006 Finnish Nationals, 6th at the 2006 European Championships, and then went on to compete in the 2006 Winter Olympics where she finished in 16th place. Although she had placed 3rd at Nationals, the Finnish skating federation had used the results of the European Championships to determine the Olympic team. Korpi, despite being barely out of juniors, qualified with her finish.