Russia both had a massive population, and eastward expansion was its natural direction of conquest for the long time landlocked Russia. Neither of those is the case for Scandinavia. It also doesn't help that unless the White Sea area and the areas east of the White Sea before Novgorod, so the 11th-12th century, Nordic expansion east directly requires Novgorod to be reduced. That is not an easy task. Moscow was lucky in that Novgorod was reliant on grain from Vladimir, so inevitably became dependent when Moscow expanded to that area. Sweden warred with Novogord a lot, and while certainly had the upper hand at time never truly beat Novgorod. A decisive enough defeat would either require an incredible military leader focusing entirely on Novgorod, and not Denmark/Norway/Livonia/northern Germany, or a case of Scandinavia uniting somehow. However even then there'd have to be some reason for this United Scandinavia to turn east instead of the places I just outlined. Then unless they really improved their agriculture to support a greater populace or avoided the Black Death, it still wouldn't be able to actually settle the vast amount of land to the east. They'd only be establishing trade outposts and vassalizing the natives. It also doesn't help that unless somehow this all occurs before Kievan Rus' conversion to Orthodox Christianity, Catholic/Lutheran Scandinavia holding Novgorod would all but guarantee Moscow, which came to view itself as the successor to Constantinople as the head of Eastern Orthodoxy and so would be compelled at some point to 'liberate' Novgorod.
To not only hold Novgorod but beat Moscow (or an alt-Russian kingdom) to Siberia is just unlikely. It's more than its simply hard. It simply wasn't a series of events that any of the Scandinavian kingdoms would pursue. Sweden at best looked to East Karelia, but otherwise focused on Estonia, Livonia, and Denmark-Norway. Denmark-Norway focused on Sweden, Holstein, Estonia. Both were pursuing dominance of the Baltic. If somehow one achieved that, they'd probably then focus on the North Sea. Geographically, all were focused on maintaining sea power. With Siberia not being the most accessible by water, Scandinavia getting involved in such a land venture makes little to no sense. It might be possible for Scandinavia to 'skip' Novgorod by water and simply go as far east as possible on water till the Arctic freezes and start from there, but their hold would never survive when the Russians expand into the area with actual force.
A scenario that might work is Scandinavia converting to Eastern Orthodoxy instead of Catholicism. If it was more connected and friendlier with Kievan Rus early in its history, it would be reasonably possible for it to fill the gap when the Mongols come and wreck the Rus. They could then follow Lithuania's example. Novgorod allies with Scandinavia against the Golden Horde, and over the centuries pushes the Golden Horde out of Rus. It also out-competes Lithuania, which had a goal of taking over as much Ruthenian land as possible till Moscow rose to oppose it. So a Scandinavian-aligned Novgorod united the Rus, and expands east.
Really, that would be more altering the Nordic identity than anything so it aligns more firmly with the Rus.