The biggest head that rolled in the great purges of the Red Army was Marshal Mikhail Tukhachevski’s. Isaac Deutsher concluded in Stalin: A Political Biography that Tukhachevski was in fact planning a coup against Stalin; Stalin had purged all his other potential opponents, and Tukhachevski planned to strike first, rightly expecting that his turn was next.
Positing no purge of the Red Army very likely means positing Stalin’s downfall and death, and Tukhachevski’s rise to head the Soviet state. That opens up all sorts of possibilities, including that of Barbarossa never being launched at all. Still, let’s say that Hitler plays it the same in this hypothetical as he did in reality.
Opinions differ on just how good a military leader Tukhachevski was. The majority view is that he was outstanding, comparable to Guderian as a mobile-warfare thinker. A substantial minority considers him overrated; he certainly had not distinguished himself in front of Warsaw, where he narrowly avoided disaster. In any event, Tukhachevski was not blind to the Nazi threat, as Stalin was; he warned the Central Committee as early as 1936 that Nazi Germany intended war on Soviet Russia. There is no possibility that Tukhachevski would have ignored the warnings from Richard Sorge, or from Leopold Trepper’s Red Orchestra spy ring, of Germany’s imminent attack.
Knowing of this, would Tukhachevski have been bold enough to launch a pre-emptive attack on the German units assembling for Barbarossa? Your guess is as good as mine. If he did so, surprise would have been complete; the German Abwehr intelligence service had completely failed to penetrate the Red Army and its intelligence was woefully lacking. The Soviet tanks were superior in both numbers and quality; their air force was huge, but neither as battle-tested nor as well designed as the Germans’. Probably it would have devolved into a bloody muddle, but Germany would have lost all chance of launching Barbarossa.
Suppose Tukhachevski waits it out instead: the Red Air Force is not destroyed on the ground in the opening days of the campaign, for Stavka has warned it and it meets the Luftwaffe in the air. The Germans probably still attain air superiority, but at a much higher price and without inflicting such terrible losses on the Red Air Force. Here a key question arises: has Tukhachevski retained the Leninist-Stalinist practice of requiring all military orders to be countersigned by political officers before they are valid? If he has, the Soviets may still lose large units to German encirclement due to time lost browbeating political officers into signing off on retreat orders. If the political officer system has been abandoned, or if the political officers have been schooled in military competence, then 1941 looks a lot more like 1942: the Soviets withdraw, trading space for time while they build up their reserves and wait for a chance to counterattack. The war is shortened by at least a year.
To sum up: if Tukhachevski launches a pre-emptive attack he probably short-circuits Barbarossa before it ever gets started. If he waits for it, he cannot “turn back” the German attack, but he possibly loses a lot fewer casualties than Stalin did and wins the war sooner.