This is a particular start for Russia. Several things are of note:
(1) China is really advanced with Paper in 850 CE and Gunpowder not long after. However they do not have Compass or Feudalism. They would destroy the Mongols and be the first to Constitution and Military Tradition. They collapsed long after taking over Mongolia (some time in the 1400s or 1500s), but before that they provided Russia with invaluable trade (see above post).
(2) Constantinople was razed by barbs. This means the Turks will be a complete non factor.
(3) No Greek/Roman supercities with tons of Wonders. The Wonders are spread out, with Oracle in Rome and Greece not having Priesthood tech on Russian start. Hagia Sophia was razed, and Apostolic Palace/Church of Nativity were not built yet.
Taking (3) into regard the first thing I did was to settle Kiev (because I can't afford the units to take it) and build the Apostolic Palace there. I faced zero competition in this - Byzantium is very weak and unstable and Spain/France did not even bother with the wonder. Then it's merely a matter of spawning a Great Prophet.
I did not settle a single city east of Moscow before Astronomy. Instead, I focused on working the Culture in my first 5 cities as high as possible to maximize the impact of the UP. Also rush teched Engineering for Notre Dame and Pikes - turns out the dozen or so Pikes I built were completely unnecessary, as the Mongols never found me until I found them after Astronomy (and they died abjectly soon after).
When one Shrine is not enough, you simply get another:
I never got voted into the Apostolic Palace because of the HRE and their UP. Nobody declared on me except HRE around 1660, which I responded promptly by taking Budapest (again, on the Oil) and they collapsed soon after the Prussian spawn.
Meanwhile, Lobachevsky uses non-Euclidean geometry to bend light:
And this facilitated my long-planned Liberalism slingshot to Astronomy. I sent a lone Caravel (upgraded from the Tireme used to contact Mali earlier) and went for the New World. Disbanded most of my Conquerors, looted Mexico a bit, then made peace. Inca peace vassalized and Aztec collapsed, the usual.
Then I moped up the Mongols after contacting them (they lost all their initial stacks to China's Bombards & Cuirassiers and their Central Asian conquerors died to Independents) and started settling Siberia, picking spots near the numerous Gems and Gold in Siberia knowing that they will be useful Corporate resources later. There is also an Oil in west Siberia. I also settled Fort Ross (Seattle) and Recife (Brazil Oil) before England and Portugal made there. I would exhaust the 2,500 or so gold in my treasury throughout a period of 250 years of settling Siberia, but I managed to tech close to Scientific Method before my economy when to a halt largely by selling techs (see previous post).
Somewhere along the way I got a random event which really helped Russia:
This made my mass Cuirassiers/Cossacks very effective against Independent Middle Eastern cities later.
I tried to cultivate England as my major ally, but Alfred's tech still really sucked and at a time England, Portugal, and Byzantium were all vassalized to Spain. Fortunately they all broke free later.
Then the Turks collapsed with the Iranians following not long after because the really powerful Mughals were pounding them. With my new Cuirassiers I switched to Occupation and quickly mopped up the lightly defended Middle Eastern Indies including Babylon (with La Mezquita and Ishtar Gate inside) along with Budapest.
Then the Russians faced some real dangers with giant Mughal stacks perched near our newly acquired Middle Eastern assets, and a materially exhausting war against Austria in the west. However, in a stroke of inspiration, I traded Economics (which I beelined for the Great Merchant needed to stop my economy from collapsing) to France and England for a total of some 2,000 Gold, and sure enough:
Diplomacy at its very finest, my friends. "Breaking the enemy's resistance without fighting" indeed.
Then the Prussian power ended the Austrian thread once and for all and I get to keep a happy and resource-laden Budapest all to myself. I teched to Constitution not long after Babylon went into full gear, and promptly built the Taj Mahal there, facilitating a switch into Representation (Hell yeah), Egalitarianism (Hell yeah), Free Market (Hell yeah), Secularism (Hell yeah), Urbanization (I miss Agrarianism, but I have to), Autocracy (just for the cost), and Imperialism (after a brief period of Resettlement during which I scrambled for even more American cities). Russia is now full steam ahead.
Now it's a glorious dash towards Scientific Method (made much easier by the Astronomy slingshot earlier) and Electricity. Americans spawned right when I was building Research Institutes everywhere. I studied the situation in North America and quickly made an alliance with England (who had become really strong by settling Canada & Australia, whereas Netherlands settled South Africa and Portugal the rest of Brazil). At this time, I already have enough land for Domination - what I need is population. I had two alternatives:
(1) Conquer more cites. I killed America (Washington and New York, for a total of 20 pop) and won Domination, but for some reason my Expansion Stability plummeted from -25 to -95 and my overall Stability from +30 (Solid) to -40 (Collapsing) due to this single act of aggression. I guess killing newly spawned civs gives you much worse stability hits? Or maybe my expansion had already hit some invisible barrier?
(2) Wait patiently for Cereal Industry to spread. After taking control of the American Great Plains it gives +6/+7 food, which really helps growth (Novgorod reached 31 pop at end game).
I reloaded my Collapsing Domination and waited for (2) while teching towards Assembly Line/Industrialism. It's surprising how long it takes for your population to increase from 30% in the world to 31%. Fortunately, the spawning of America, an extra civ, seemed to have lowered this required threshold from 32% down to 31%.
Finally I won in 1800. America demanded Fort Ross/Seattle in a Congress and naturally war were declared. However the Anglo-Russian alliance really paid off there and only America and Thailand (pfft who cares) declared on us. I also bribed Spain (who hates my guts as usual) to declare on Netherlands earlier, which kept them busy.
The core of Mother Russia:
And her unquestionable dominance over the world:
With her legendary cities:
And her gargantuan economy:
I hadn't planned on winning this early, so I only got Combustion a few turns after winning. But I do have a total of 14 Oil inside my Cultural borders, which would translate into a +35

Oil Industry and a +41

Computer Industry respectively.
I don't have time to tech to Environmentalism either, but you see the number of Forest Preserves and Windmills. If you play this Russia till end game of course you'll win UHV & Space Race blind-folded.