That's the popular narrative, but it really seems like Soviet propaganda. Stalin wanted to attack Germany in 1937 when Hitler annexed the Sudetenland, but UK and France refused to stand up to Hitler. After the Munich conference, Stalin began tearing down all the factories west of Moscow and rebuilding them east of the Urals.

If you look at any of Hitler's speeches or writings, he always talks about expanding eastward. Stalin had known for years that Germany will attack. After the annihilation of Poland, there's plenty of stories about Polish citizens warning the Soviets of an impending invasion. The Soviets were well aware that the Germans were planning to attack.

However, the Soviets performed very poorly in the first few weeks of the war. Stalin claiming it was a surprise and betrayal by Hitler sounds like an excuse for losing tons of ground and men.