You don't need population or transportation to claim an area. The Mongols completely proved you wrong here. I've already claimed the areas around Lake Baikal.
you dont have enough man to support that so called claim, you barrly have enough man to populate your land now. (guss you shouldnt kill all your man as russia you kek) also the mongols didnt, they got a nice streak and then just collapsed, it took a great man to actually keep them at that state and when he died no one could actually do that.
You don't need men to claim an area. You can still claim it. Who cares if I don't have enough men to populate my areas? I still have them claimed. That's like saying Wyoming shouldn't be a state. It houses 500,000 people and the state is around 1/3 the size of Texas. The Mongols claimed a massive amount of land, they could barely support it, but they did. Most of the land that Genghis Khan conquered was given to his sons who created massive empires/sultanates.