I understand that only in 1924 did the Bolsheviks finally hold a firm grip on power in the USSR and by 1930 might not have made foreign affairs their prime objective. Yet I remember hearing about the not as popular First Red Scare and wonder how exactly the USSR went from internal fighting in 1924 to having communist parties in nearly every government in Europe at least, if not the US, China, and Japan; which in turn led to Mussolini creating fascism as a response to push Socialism back.
This question has a number of incorrect precepts underpinning it. The formation of the USSR and the solidification of the Bolshevik's hold on power was an important event in the history of communism, but this history did not begin in 1924. Communist and Marxist parties had a long pedigree before 1917 and often formed around localized issues and grievances. Moscow tried to coordinate a number of these parties through the Comintern, but this was much easier said than done. The Comintern could not erase the localized context of these parties and this created a very complex batch of politics in the interwar period.
To belabor a point, most of the interwar communist parties traced their genealogy back to the prewar period and the nineteenth century. Marxist parties had formed in the nineteenth century in various European states and had a very fractious unity in 1914. The Bolsheviks, for instance, grew out of the Russian Social Democratic Labor Party (RSDLP), a Marxist Russian political party that was prone to shifting factions and alliances. Many of Europe's socialist parties had a similar degree of disunity behind the edifice of solidarity over the problems of capitalism. One of the fracture points in pre-1914 French socialism was over whether the political movement should focus on a pragmatic working within the French political system at the risk of selling out the ideals of socialism. Other Marxist parties emerged as specific responses to colonial and foreign rule which imparted a nationalist character to their ideology that was somewhat at odds with orthodox Marxism which tended to eschew nationalism as a tool of capitalism. Polish and Jewish socialist parties in the Western Provinces and the Pale of Settlement all had to reckon with the national question and defined who fit in their vision of a more just socioeconomic order. The various non-European parties also had a strong anti-colonialist and national bent. A number of East Asian intellectuals gravitated towards Marxism as modern ideology that explicitly condemned colonialism while hewing to a vision in which scientific reformism would alter the old order.
The First World War exploded fractious solidarity and sharpened existing tensions within the global left. Many of the mainstream leaders of Western and Central European socialist parties voted for war credits in 1914 and some argued that the national victory would be a victory for socialism. A good many of the rank and file of these parties as well as a number of firebrands rejected this approach and this grew only as the war dragged on. The German SPD was an example of this phenomenon. Disaffected SPD activists came to reject the party leadership's conciliatory attitude and coalseced into an independent-minded faction, the Unabhängige Sozialdemokratische Partei Deutschlands (Independent Social Democratic Party of Germany/USPD). The Russian Revolutions in 1917 were both a catalyst and a pretext for USPD activism within Germany. Events in Russia showed that it was possible for there to be an actual revolution by the masses. This had been one of the key stumbling blocks for Marxist parties since the nineteenth century in which some Marxist promised a revolution that did not ever seem to arrive. Additionally, the location of the 1917 revolution- Russia- was also a sign of hope. Russia had the reputation as being the most repressive and reactionary of European states and the idea that revolution could have sprouted there gave hope to a number of like-minded left-wing activists. The USPD's leadership thought they could replicate Lenin's seizure of power and they often framed their activism as being part of a global proletarian rejection of the war and the governments that enabled the conflict in the first place.
The SPD-USPD split became even more complicated in the German Revolution of 1918 in which the USPD splintered off into different factions including the more militant Kommunistische Partei Deutschlands(Communist Party of Germany/KPD) and the SPD's leadership saw its chance to take the reins of power. The SPD was the major political partner in the post-1918 German government and a number of its politicians such as Gustav Noske helped to suppress USPD and KPD revolts. This suppression was quite bloody and involved extrajudicial murders and the use of far-right Freikorps militias. This suppression stopped the attempts by the USPD and KPD to overthrow the government, but could not eliminate the movement itself and a majority of the USPD voted to join KPD in 1920.
This (very oversimplified) view of the events in Germany between 1917 and 1920 illustrate that Moscow inherited a very complex situation among the global left. The Soviet Union's position as the government that was born out of a worker's revolution made it a de facto leader for Marxist parties around the globe and Lenin and company were more than happy to play this role. The 1919 formation of the Comintern began even before the Reds' victory in the Civil War. But the relationship between Moscow and the various non-USSR communist parties was not one of center-periphery rule with the Kremlin calling the shots. A number of non-USSR activists brought their own concerns to Moscow and did help shape policy. Although the Bolsheviks were roughly aware of American racism, it was actually black activists that brought lynching and other problems of Jim Crow to the attention of Moscow. Black radicals from the US and Caribbean brought up the issue of racism in the Americas during the 1st Congress of the Comintern in March 1919. The Fourth Comintern Congress authorized a "Negro Bureau" three years later and under its auspices published a number of tracts attacking the racism and publishing books like Negroes in America and Lynching in America by Claude McKay. These books had a limited print run in both Russian and English. McKay was a Jamaican-American poet and author whose dark skin meant that he was an ideal poster-child for the Soviet's antiracist ideology. Soviet publications in the early 1920s often featured McKay with Soviet leaders. The USSR's leadership soon recognized the propaganda value of antiracism and this remained a consistent theme of Soviet propaganda through 1989, but it had this campaign had non-Soviet origins and few of the Bolsheviks gave much thought to the plight of blacks in the American South.
The complicated dynamic between the USSR and various Marxist parties in the 1920s was not so much one of dominance and subordination but rather synergy and dovetailing ideology. Moscow and the Comintern would always try to tip the scales in favor of pro-USSR leaders within various communist parties and this meant a number of parties became increasingly pro-Soviet as the decade wore on. Yet the pro-Soviet attitudes of the parties was not wholly a product of Moscow's interference. The romance of 1917 and the achievements of the USSR were powerful appeals for many within the global left, especially since reports of the less than savory aspects of the USSR's dictatorship could be written off as dishonest counterrevolutionary propaganda (of which there also was a lot floating around) or even as typical Russian moroseness over the pain of exile. The Comintern's mission was to coordinate and set goals for various communist parties, but there were times where its policies were what most of parties' leadership wanted to do anyways. A number of commentators in the 1930s and beyond have blamed Moscow for the KPD's refusal to cooperate with the SPD in the light of the emerging threat of Nazism, but while Moscow certainly did hamstring efforts any potential KPD-SPD coalition in the 1930s, the KPD needed little prompting in this direction. The bad blood over 1918/19 and Noske ran deep within the KPD leadership and distrust of the SPD did penetrate into the rank and file of the KPD.
Moscow certainly welcomed the onset to the global economic crisis and many among the global left saw the economic downturn as a harbinger of capitalism's final contradictions working themselves out. But the Soviet Union did not create the Depression. Moreover, the Depression itself seemingly validated many of communism's precepts that capitalism was an unworkable system. Communist parties around the globe were able to increase their memberships and gain a hitherto degree of currency among the unemployed working classes and intellectuals. In the US, this manifested itself not only in various communist discussion circles, but an increased communist party presence in labor activism. The advent of fascism in Germany along with the preexisting dictatorship in Italy as well as various far-right parties in Europe heightened the sense that communism was at the vanguard of the fight for human freedom. Both Hitler and Mussolini positioned themselves as the ideological archenemies of Marxism and this lent communism a further degree of legitimacy to those wishing to fight fascism.
Counter-intuitively, Moscow greeted this grassroots communism in the Depression with a degree of apprehension as it tried to assert control and impose discipline to get these groups to hew to the Comintern party line. This was successful only to a point; while Moscow played an outsized role in party leaderships and official platforms, ground-level activism tended to be more divorced from high politics. Local conditions also were very important to party memberships; in the case of the US, the Depression and the fight against fascism were two of the key catalysts for its increased membership. The removal of both coupled with the Second Red Scare turned the CPUSA into a very marginal fringe party on the American political scene, even among the American left. The USSR really did not do that much "to plant seeds of communism" during the Great Depression. The Depression itself did much of that work for the USSR.