2009-10: Vyacheslav Osnovin skated for Traktor Chelyabinsk U16 in Russia. He scored 12 goals with 25 assists and had 10 penalty minutes in 28 games. Traktor finished first in the region. In the regional U16 tournament he had 1 goal with 3 assists and was minus-five in five games as the Ural team finished fourth in the six-team tournament. Traktor finished second in Group B in the Russia U16 championship. In three games Osnovin scored 1 goal with 2 assists and was plus-one with 8 penalty minutes.
2010-11: Osnovin was the leading scorer for Traktor (1994-born) in Ural Region play and represented Russia at the U17 Four Nations Cup in Illinois and at the European Youth Olympic Festival. In 32 games in regional play he scored 25 goals with 39 assists and had 36 penalty minutes. Skating for Traktor at the U18 national championship tournament, he scored 4 goals with 2 assists in six games as the squad won the bronze medal game. In international play, Osnovin scored 1 goal with 1 assist and had 8 penalty minutes at the Four Nations Cup and had 1 goal with 1 assist in three games at the EYOF. He was selected by Traktor Chelyabinsk in the first round (sixth overall) of the 2011 KHL Draft.
2011-12: Osnovin played for Belie Medvedi Chelyabinsk in the MHL (Russian U22 league) and represented Russia in international play at four tournaments. In 45 games MHL games he scored 7 goals with 18 assists and was minus-seven with 36 penalty minutes. Belie Medvedi was forced into play-out play after finishing 24th in the 30-team league. Osnovin played in two of six play-out games and was plus-two with 2 goals and 1 assist. Playing for Russia, he had 1 assist with 27 penalty minutes at the 2011 U18 Ivan Hlinka Tournament and had 3 goals with 1 assist in three games at the Sergei Zholtok Tournament. Osnovin had 1 goal with 1 assist at the U19 World Junior A Challenge. He was an assistant captain at the U18 World Junior Championship and scored 1 goal with 2 assists and was plus-two with 29 penalty minutes in six games. Russia finished fifth in the tournament. Osnovin was invited to the 2012 NHL Draft Combine and was ranked 14th amongst European skaters in Central Scouting's final rankings prior to the 2012 NHL Draft.