The figure head of SiOC has to be Stalin, but he was definitely no slouch when it came to spreading the revolution. The Soviet union invaded Finland, The Baltics, Romania, Poland, Mongolia, Iran, and Xinjiang. they also gave significant support to the Chinese, Korean, and Spanish revolutions. interestingly enough, all those invasions are basically universally denounced by Trots. Regardless, they represent the USSR invading practically every country it bordered and every important socialist revolution of the time apart from the Greek partisans.
So as I see it, what else could they have done?
Declared war on the United Kingdom in the 1920s? obviously a disaster, once the Soviets lost in Poland, I don't see how anything like this could be held as viable, but you can also blame Stalin for losing in Poland, if you wish.
Declare war on Fascist Germany sooner? the Soviet Union wasn't ready to fight Hitler in 1941, let alone the 1930s. They had no border with Germany, and Poland refused them when they did consider an invasion of Germany, but I guess you could argue the war would've gone better earlier when Germany hadn't fully remilitarized, and didn't have GPMGs, or Czech tanks or Romanian oil.
Spurn the Capitalist world and refuse to do partnerships with Germany and the USA? Frankly, the partnerships and expertise they received from the USA in the 1930s were critical to defending from the Nazis. We've seen how socialism develops when you try to replace capitalist technology with the revolutionary enthusiasm(which the soviet union wasn't immune to either, see "Soviet Tempo") and the result is backyard furnaces and backsliding.
Edit: And trade with Nazi Germany? Cotton for Heavy Machinery is not, I think, a morally bankrupt deal. Oil for Heavy Machinery is more concerning, but again, the Soviet union was not ready to fight Hitler even in 1941. if you embargo a country, there can be consequences. just months after Barbarossa, Japan declared war on the United States because of an oil embargo against them.
Yes, the Soviet Revolution was eventually crushed and ended in ignominy less than a century later, and it was precisely because they couldn't overcome their being under siege for their entire existence, but I still don't see how a rapid war to defeat foreign capitalism is given as a viable suggestion.
I'll try to keep it short.
In the midst of the 1905 revolution, Trotsky dreams up this idea that in underdeveloped countries workers have to play the role of the democratic revolutionary forces because the national bourgeoisie are incapable of it. In this theory, since the workers are in charge already, they can/must carry out the revolution all the way through (thus making it permanent). I think importantly here for Trotsky, just because Communists are in charge doesn't mean it's socialism.
In 1924, after Europe begins to quiet down, Lenin dies and Stalin begins consolidating power in the CPSU. Domestically this was the height of the NEP which was seen kind of like a truce with the semi-bourgeois peasantry. Internationally (in what is known as the "Second Period"), Comintern policy begins to shift away from "The international worker's revolution is imminent" because it clearly wasn't. The new direction was characterized by:
Trotskyists would also characterize the Second Period as the beginning of the USSR exercising strong control over foreign Communist Parties, bureaucratization, and being extremely right wing (for a Communist Party). The third point is probably where the largest break with the theory of Permanent Revolution is. Trotsky and his followers were strongly in favor of Communists standing on their own (or with less radical workers in a united front) as opposition to all bourgeois forces. Perhaps the most famous instance of this break is in China where the Communists were directed to support the Kuomintang and they got burnt badly for it (though I would argue the KMT would have turned their sights towards the Communists regardless)
Socialism in One Country was of course an attempt to reconcile that the "grand prophecy" of the international worker's revolution didn't happen after 1917 and the USSR basically stood alone. Navigating reality on both international and domestic fronts required pragmatism and a degree of cooperation with the capitalist powers of the world.
The theory of Permanent Revolution wasn't that the USSR should have been invading and establishing socialist states in other countries. It's more so that the Comintern (which was dominated by the USSR) should have maintained a more revolutionary line internationally. As we get into the Third Period of the Comintern and then the Popular Front we see the focus shift towards fascism and social democracy. Those debates resemble this one but I've already written too much.
What does this mean practically? The Soviet Union being more Rhetorically proselytizing in the League of Nations? Conducting itself with the moral character that will inspire foreign proletariat to rise up? Covertly sending (more) money and advisors to communist parties in capitalist countries? building revolutionary parties to lead uprisings sooner, like the Yugoslav Communists tried and failed at during the Interwar period? The philosophy seems coherent, but I'm struggling to think of what actions they thought were being unfairly deferred, which at all seemed remotely viable with the retrospective they had even then.
I'm not entirely sure. I've not read it but the answers are probably in here https://www.marxists.org/archive/trotsky/1928/3rd/index.htm