A neutral power cannot make a move into a neutral territory (E40 rulebook, pg 15, “Powers Not at War with One Another” side bar, under “Neutral Powers”)
The Soviet Union is still considered to be a neutral power on the Europe map even if it is at war with Japan (E40 rulebook, pg. 37, continuation of Soviet Union’s “Political Situation, National Objectives, and Bonus Income”, under Political Situation)
Taking both of these rules together, the Soviet Union must be at war with either Germany, Italy, or both to move into any neutral territory, pro-Axis, pro-Allies, or strict on the Europe Map.
So the answer to your question is a definite no.