Some Russians supported the Bolshviks because they felt they offered a chance to escape the miserable living conditons imposed by the tsarist regime.
The Bolsheviks overthrew the government in a coup d'etat in the Bolshevik Revolution.
because they had the support of public.
The Bolsheviks and Vladimir Lenin wanted to overthrow the government because a lot of Russians were killed in World War I and Russia had social and economic problems.
During the Russian Civil War the US and other Western powers sent expeditionary forces into Russia to help those that were fighting the Bolsheviks, the white Russians, through equipment, training and manpower.
"Peace, Bread, and Land"
The Russian Revolution of 1917 was primarily funded by various groups opposed to the Tsarist regime, including the Bolsheviks, who received financial support from exiled Russians and sympathizers abroad. Notably, the German government is believed to have provided funds to the Bolsheviks to destabilize Russia during World War I. Additionally, wealthy individuals and organizations within Russia, as well as other revolutionary factions, contributed resources to further their causes.
They didn't worry about support. If you were against them you disappeared, was sent to a work camp, or killed. Very simple.
The Bolsheviks promised the Russian peasants land redistribution, aiming to eliminate the feudal system that had oppressed them. They advocated for the transfer of land from wealthy landowners to the peasants, which resonated deeply with the agrarian population seeking a better livelihood. Additionally, the Bolsheviks pledged to address issues of poverty and provide support for rural development, thus garnering significant peasant support during the Russian Revolution.
The Slavic people were the same ethnic group as the Russians, so they wanted to support them against Austria-Hungary, whom Russia was fighting land for.
In George Orwell's "Animal Farm" the Bolsheviks are represented by the pigs.
The Russians had to pull out for several reasons during World War 1. Primary reason was the civil revolution which was going on in Russia. The secondary reason was lack of funding and the distance required to supply and fight the war was too great. Another reason was that the Tsar was killed by the Bolshiveks.....communist forerunners of the USSR. They didn't have to. They chose to, because the war served no purpose for them and doing so increased political support for the Bolsheviks.
In (and even before) 1917 in Imperial Russia, the Bolsheviks gained mass-support for numerous reasons. Most of the reasons, however, centered on the corruption, inefficiency, and failures of the Russian royal dynasty and its administration as the governing power in Russian.