Kostin made his international debut at the 2016 IIHF World U18 Championships, serving as captain of the Russian U-18 team. He recorded four assists in five games as the team finished sixth. Later that year he participated in the 2016 Ivan Hlinka Memorial Tournament, an under-18 tournament not sanctioned by the International Ice Hockey Federation but considered a top tournament for the age group. Again captain of the team, he had four goals and three assists in five games as the team won a bronze medal. He also played in the &lt;a href="CHL%20Canada/Russia%20Series"&gt;CHL Canada/Russia Series&lt;/a&gt;, an annual tournament between CHL All-Star teams and the Russian national junior team, scoring two points in five games.