As people have been saying, there a variety of reasons that while not impossible, this is unlikely, and will probably mean a peripheral and foreign-dominated state (Trans-Amur/Trans-Baikal propped up by Japan, Crimea or Yugorussia propped up by the Entente).
The Whites were never in any sense a united, co-ordinated army. Ideologies and willingness to compromise on them were never clear (the movement's official manifesto was "We'll get back to you on that"), which prevented much state infrastructure not connected to fighting the Reds building up. That along with their superior organisation and control of the industrial heartland of Russia was they the Reds won.
So besides OTL's "Reds beat everyone except the most united, organised, geographically advantaged, foreign-supported nationalist factions", the other really plausible options are "the Red government goes under in 1919, Russia fragments altogether ala China" or "rump White state held up on the peripheries somewhere". You'd need to make Britain and France way more willing to get decisively involved. Perhaps a foreshortening of WW1 overlapping with an RCW butterflied about to give the Whites more advantages?
You could probably make such a state in Ukraine of the Far East monarchist, if you get the right generals in the right places. The Whites didn't let being reduced to Vladivostok and a few adjacent towns prevent them from declaring restoration. Most, however, would despite their own convictions probably see the writing on the wall.