[3] Kosti trained throughout her swimming career for Olympiakos sports league in Athens under the tutelage of her coach Markos Mantaloufas.

Kosti made her Olympic debut as part of the relay team in the women's 4 × 100 m freestyle with Zoi Dimoschaki, Martha Matsa and favorite Nery Mantey Niangkouara, when Greece hosted the historic modern Games for the second time in Athens.

She swam the anchor leg on the outside lane in heat two, but her team was disqualified due to an early relay takeoff by Matsa.

[4][5] In 2005, Kosti helped her Greek teammates Dimoschaki and 2000 Olympians Aikaterini Bliamou and Zampia Melachroinou atone from their Olympic disqualification in Athens to relish for a bronze-medal victory with a 400-metre freestyle relay final time of 3:49.70 at the Mediterranean Games in Almería, Spain.

[9][10] Two days later, in the 100 m freestyle, Kosti escaped from the bottom of the field to finish heat three in seventh position and thirty-seventh overall with a time of 56.44, edging out Slovenia's Nina Sovinek by almost a full second.