There was some serious work in that direction in the 1920s, but with Stalin's ascent to power, left-wing education and indoctrination were in fact stamped out, to be replaced with Russian crypto-nationalism, imperial and militarist sentiment, and most notably an Asian-style cult of the god-king.
In fact, by the end of his life Stalin had uprooted or completely subverted virtually every institution that the 1920s' Old Bolshevik leaders introduced (with the sole exception of the repression apparatus, which he expanded while purging most personnel) - from the "New Economic Policy" and legal free abortion (!) to the avant-garde artists' organizations and the Comintern.
I'm not necessarily saying that those institutions were good (although the NEP objectively worked well enough); I'm saying that, since around 1930 and until the end, Soviet leadership only paid lip service to genuine radical indoctrination/reeducation, preferring the old staples of nationalism, feudal loyalty and leader-worship.

Later, in the Brezhnev era, an official cargo cult of sorts was formed around Marxist phraseology and such, but no-one gave a shit whether, say, the "Marxism-Leninism" classes at universities were even functioning as propaganda.
In fact, it was rather counter-productive as propaganda, as people began to mock even the several objective, verified achievements that it trumpeted - like the space program or the considerable infrastructure investment. The system became too stagnant even to attempt self-replication through indoctrination.

So there. The USSR was mostly an ineffective (if somewhat orderly) conservative regime that would have shat its collective pants if a New Soviet Man suddenly appeared in flesh.
And hey, a handful did appear, more or less by accident; e.g. Andrei Sinyavsky, Yuli Daniel, Vasily Grossman (Socialist Realist writers!), Sakharov, the Strugatsky brothers, numerous other good people who advocated left-wing ideas and got suppressed by an ostensibly socialist system. Oh, well, for the wider Warsaw Pact, I guess Zizek also counts as a New Soviet Man :)

P.S.: lengthy quote incoming! Orwell's praise of left-wing indoctrination in Homage to Catalonia.

In practice the democratic 'revolutionary' type of discipline is more reliable than might be expected. In a workers' army discipline is theoretically voluntary. It is based on class-loyalty, whereas the discipline of a bourgeois conscript army is based ultimately on fear. (The Popular Army that replaced the militias was midway between the two types.) In the militias the bullying and abuse that go on in an ordinary army would never have been tolerated for a moment. The normal military punishments existed, but they were only invoked for very serious offences. When a man refused to obey an order you did not immediately get him punished; you first appealed to him in the name of comradeship.

Cynical people with no experience of handling men will say instantly that this would never 'work', but as a matter of fact it does 'work' in the long run. The discipline of even the worst drafts of militia visibly improved as time went on. In January the job of keeping a dozen raw recruits up to the mark almost turned my hair grey. In May for a short while I was acting-lieutenant in command of about thirty men, English and Spanish. We had all been under fire for months, and I never had the slightest difficulty in getting an order obeyed or in getting men to volunteer for a dangerous job. 'Revolutionary' discipline depends on political consciousness--on an understanding of why orders must be obeyed; it takes time to diffuse this, but it also takes time to drill a man into an automaton on the barrack-square.

The journalists who sneered at the militia-system seldom remembered that the militias had to hold the line while the Popular Army was training in the rear. And it is a tribute to the strength of 'revolutionary' discipline that the militias stayed in the field-at all. For until about June 1937 there was nothing to keep them there, except class loyalty. Individual deserters could be shot-- were shot, occasionally--but if a thousand men had decided to walk out of the line together there was no force to stop them. A conscript army in the same circumstances--with its battle-police removed--would have melted away. Yet the militias held the line, though God knows they won very few victories, and even individual desertions were not common.