Koutsioumpas emerged himself into the international scene at the 2001 Mediterranean Games in Tunis, Tunisia, where he took home the silver medal in the men's 130-kg division.

When Greece hosted the World Championships in Patras later that year, Koutsioumpas enchanted the home crowd in a spectacular fashion, as he beat Bulgaria's Sergei Mureiko at 8–0, and ran off the mat with a bronze medal.

When Greece welcomed the 2004 Summer Olympics in Athens, Koutsioumpas qualified as a member of the Greek squad in the men's 120 kg class, by placing fifth and receiving an automatic spot for his home nation from the 2003 World Wrestling Championships in Créteil, France.

[4][5][6] Koutsioumpas suddenly lost a 2–2 draw to Kazakh wrestler and 2003 world bronze medalist Georgiy Tsurtsumia on his opening match, but quickly rallied with and delighted the home crowd inside the Ano Liossa Olympic Hall, as he prevailed two straight matches over Sweden's Eddy Bengtsson and Georgia's Mirian Giorgadze (both at 5–0).

[7] At the 2005 Mediterranean Games in Almería, Spain, Koutsioumpas scored a stunning 7–5 to climb the summit of the podium and snatch the men's super heavyweight title in his final match against Turkish wrestler and defending champion Yekta Yılmaz Gül.