Asha Gigi made her debut over the marathon distance in 2003 at the San Diego Marathon, where her time of 2:31:39 hours earned her a place for the national team. At the 2003 World Championships in Athletics in Paris she came 19th and was part of the Ethiopian silver medal-winning team in the IAAF World Marathon Cup competition. The year after she was a lowly tenth at the Osaka Ladies Marathon but then made a breakthrough at the Paris Marathon, setting a personal best time of 2:26:02 hours to finish runner-up to Salina Kosgei. She had her first Olympic selection, but did not manage to finish the marathon at the 2004 Athens Olympics. She also ran at the 2004 New York City Marathon, but managed only 13th place.