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I really do doubt that the Soviets would have been able to make it a surprise attack in 1941. Just too much in the way of German preparation and expectation of the Soviets to strike.
The one thing I would say is that German intelligence appears to have become more brazen as Barbarossa neared; a report on June 13th (a Friday) determined that there seemed to be some Red Army reinforcement of the frontiers going on but this was dismissed as irrelevant, too late in the game. If the Soviets had began their build-up in May and played a very good deception game then I think there's at least a chance they could have caught the Germans off-guard.
What one really needs is for something to cause a distraction at the crucial time. May 1941 involved the Bismark's enterprise, for example. Have Bismark and PE evade Norfolk, Suffolk, and POW after the Hood, and start to cause issues in the Atlantic while the British seek it in the expanse of the Atlantic, and it's possible German eyes will be at least flickering westwards as well as eastwards. The Army will still be looking towards the Soviets, but those higher up the chain might be less focused.