In practical terms:
1st, Peter I abandons idea regarding the Baltic coast and concentrates exclusively upon the South & South-East directions of expansion because they can provide the greater land mass acquisitions. As a pre-requisite of the earlier success, he need to modernize his army with the Ottomans as the main enemy in mind: in OTL his attempt to fight them with the "anti-Swedish" army proved to be a failure but within few decades the winning tactics had been developed with essentially the same technology and, he had to pay more attention to the available existing experience of Charles of Lorraine and Prince Eugene. However, the eventual OTL winning formula for the Russian army was quite simple and consisted of 2 main components: (a) to have troops trained to act aggressively relying more on a bayonet (for infantry) and sword (for cavalry) than on fire and (b) find where enemy is an attack regardless the odds. In other words, ideas absolutely opposite to those used for training Peter's army and much easier to implement. Something should be done about cutting the huge baggage trains, arranging for the longer and faster marches and, preferably, introduction of the uniforms which look less "western" but much better suited for the Russian troops (and the new theaters of war). This may take a couple years after the Peace of Constantinople (1700) - let's assume that Peter did analysis of his Azov campaigns and came to the right conclusions rather than being born a genius who knows everything in advance.
2nd, in 1702 - 03 Peter attacks the Crimea (pretext always can be found), crosses the steppe by the fast marches and attacks Perekop fortifications, which were a joke: 10 kilometers long dry moat and earthworks which nobody did or could seriously defend and in the middle a single small stone fort. In OTL in 1736 Munnich simply crossed the moat, got to the fort from the rear, took and destroyed it (the whole storm operation took a single day). Just for the fun of it, Peter may have a parallel attack by crossing Syvash entry at Genichesk and marching by Arabat Split to the "rear" of the Crimean Peninsula and taking Kerch and Feodosia while the main army marches toward Bakhchisaray. If his troops on the same level of the logistical efficiency as those of 1768 - 74, this is not a big deal (in 1735 - 39 Russians occupied the peninsula but had been defeated by a lousy logistics).
3rd, the next steps are: (a)
occupation of the Northern coast of the Black Sea (capturing Ochakov and few more fortified places) and then (b) moving the main theater of operations on the Danube. After the main Ottoman armies are defeated, the Russians are
occupying Moldavia, Wallachia and Bulgaria (Constantinople being an option but not a necessity). At that point peace with the Ottomans is signed. Unlike numerous OTL cases, in that AH the rest of Europe is busy fighting WoSS and can't interfere on Ottomans' behalf.
4rd, taking an advantage of the turmoil in Persia, Russia is easily annexing
Azerbaijan and both
Ottoman and Iran held parts of Armenia (don't remember which of them owned what exactly at that point).
5th, the first expeditions into the CA started but their goal is land grabbing (even if initially on a smaller level).
At that time Peter dies. During the reigns of Peter's successors Russia keeps staying out of the European entanglements and concentrates exclusively on expansion in Asia. As a result, the OTL Russian borders there are established by the late XVIII - early XIX (I'm not sure that expansion into Afghanistan makes sense). Then Russia expands into
Eastern Turkistan and
Mongolia, "fixing" Russian-Chinese border established by Nerchinsk Treaty.
Government sponsors the road construction (yes, I understand that for XIX century Russia this is almost ASB

) and resettlement (of the personally free peasants) to the Eastern areas to create at least some base for the future conquest of (the whole) Manchuria in the early XIX with a potential annexation of Korea.
The Western Europe keeps fighting its wars ....
Ah, yes. At some point Austria and Prussia decided to get pieces of the PLC and Russia reluctantly agrees ending up with Belorussia (
we are still in a race for a landmass 
). But not Poland or Lithuania (so Prussia and/or Austria will have that pain in their butts).
Alaska is in the Russian possession on OTL timeline and, with an earlier firmer grip on the Pacific Coast, Russians are getting more ambitious and are grabbing a big chunk of California from Spain (there are not too much of a Spanish military presence there so the claim is mostly of nobody's lands).
Are we almost there in the terms of a landmass? Probably not quite yet, but the initial premise is misleading because by the time of its greater extent the Mongolian empire ceased to be a single state in anything but name.
Well, let's say that while Britain and France are still trying to figure out who has a bigger p... oops hand, Russia invades Persia and conquers Kurdistan after which attacks the Ottomans
in Asia (so that nobody can interfere) and conquers, in the modern terms,
Iraq.
It already grabbed all Armenia in the XVIII so it is not a big distance to Syria and Mediterranean coast, especially if there is a handy uprising somewhere in the Ottoman Empire so shall we say Norther Syria and Antakya. BTW, in OTL Russian Mediterranean expedition took Beirut in 1773 so you can add some naval acquisitions as well.
Hopefully, the mission is accomplished.....