Couple possiblities:
1.)Russia conquers China/India or part thereof
2.)Russia adopts a very pro-immigration and natalist policy early in the 1900 and grows dramatically. The former would likely need to have a democratic Russia to succeed.
Immigration policies only work if people want to go to a country and there is a compelling need.
Why would anybody want to move to Russia? Russia is a source of immigrants, not a destination, except recently following the collapse of the USSR between the periphery to the core. The only people with worse living standards in the early 1900s are people in the colonies/China/some parts of Latin America/some parts of the Balkans/Empire Ottoman - and even for a lot of those it isn't like they're that much less developed than the Russian peasantry - and they have no reason to go to Russia instead of somewhere else. It is labor-abundant anyway too, so those people are unneeded.
Pro-nationalist policies are also a lot hard to implement than they sound; financial benefits are the easier to conceive (haha, I am such wit) of, but their effects are limited and for a state like Russia they're expensive. Some of the social policies can happen too, but those are more nebulous.
I'd say the best way for Russia to reach such a huge population, starting from the base of the Russian Empire and without any major territorial acquisitions is to do the standard delayed development approach that has sometimes happened in Africa/Latin America/parts of Asia, where they have basic medical technology so as to drop the death rate, but it takes them a really long time to then bring down the birth rate and develop economically. Given that this is one of the paths which gets discussed on Russia in the event of the Communists not appearing, where people speculate they'd be like a geographically massive Mexico, this might not necessarily be impossible. Given that Mexico started off the century with around 13? million people and now has 120 million, they actually work pretty well as an example of how to get a huge population; similar levels for the Russian Empire would clear it of 1 billion by a substantial margin.
As far as food, Russia has a huge territory, especially if the Russian Empire remains around; its rare that nations are limited in their population growth by food supplies any more. Provide their agriculture isn't a complete disaster, and its hard to do as badly as Soviet agriculture did, they should be fine.
If we're referring to 1700 POD I'm sure there are a huge number more things, but this is a post-1900 forum after all, so therefor I want to stick to post-1900 ones.