His first outing at a major event was at the 2002 IAAF World Cross Country Championships. He finished ninth in the junior race and shared the team silver medal alongside race winner Gebregziabher Gebremariam. Two years later he began making an impact in the senior ranks by winning the silver medal in the 10,000 metres at the 2004 African Championships in Athletics behind Charles Kamathi. He was selected to represent Ethiopia at the 2004 IAAF World Half Marathon Championships and he finished in tenth place. He fared better the following month as he helped his country to victory at the International Chiba Ekiden in Japan and then won at the Great Ethiopian Run in a course record time. Dinkesa ended the year with a win at the Iris Lotto Cross Cup in Belgium.