Revolutions...
The experience of France in 1792-94 shows that a popular revolution can successfully defend itself against often superior external forces if for no other reason than the population might fear the revenge of those they had overthrown.
For a "White" campaign to have succeeded, I think you need two changes. First, a less successful Bolshevik revolution so that the closing of the Constituent Assembly in January 1918 forces Mensheviks, SRs and others to take up arms against the Bolsheviks. More important, you need the Whites NOT to be some group of ex-Tsarist army officers but a more broad-based coalition to which groups like the Mensheviks and SRs could join. In other words, an anti-Bolshevik front rather than a counter-revolutionary front.
Let's suppose that such a broad-based coalition comes into being in the spring of 1918 with the Mensheviks leading protest in the towns, the SRs in the countryside and Yudenich and others fighting the Red Army directly.
By the Autumn of 1918, facing defeat and retreat on a number of fronts, the Bolsheviks face growing insurrection and desertion in the cities. On November 9th 1918, Trotsky is killed in a skirmish with anti-Bolshevik troops south of Moscow. With the war ending in the West and the prospect of British and American intervention and with growing civil disorder in both Moscow and Petrograd, Lenin loses his nerve and flees Russia leaving Stalin to face the end as anti-Bolshevik armies gather around Moscow for the final battle.
On December 10th 1918, the last Bolshevik stronghold in Moscow has fallen, the city is in ruins with thousands dead among them Stalin. In Petrograd, a new Provisional Russian Government is formed which immediately calls elections for a new Constitutional Assembly.
The elections show the Social Revolutionaries and Mensheviks to be the most powerful bloc, opposed by a strong Peasants' Party. The SR leader becomes the new Prime Minister of the Russian Republic on March 1st 1919.