After playing youth hockey with Sputnik Nizhny Tagil, Soshnikov was chosen in the sixth round, 123rd overall of the 2010 KHL Draft by Atlant Moscow Oblast.

Upon completion of his second season in the KHL, on 20 March 2015, Soshnikov decided to move to North America to play in the NHL, signing as an undrafted free agent to a three-year, entry-level contract with the Toronto Maple Leafs.

In addition to this, he is now no longer waiver-exempt, meaning he would have to clear through waivers if he were to be sent back down to the AHL[3][4] However, a logjam of players meant Soshnikov saw limited action.

[8] As an impending restricted free agent from the Blues and unable to cement a role within the NHL team following an injury plagued 2018–19 season, Soshnikov opted to return to Russia to hone his game in the KHL.

After four games in the AHL, on 19 December, Soshnikov cleared unconditional waivers, resulting in the mutual termination of his contract with the Islanders.