I think the best you can manage is a delay rather than a full stop. Certainly enough turmoil can be thought up to keep the Russian state unstable through, say, the 17th century.
(Off the top of my head, the Ottomans advance through the Caucasus rather than the Balkans forcing the Russians to defend their southern border. You get a more stable Eastern Europe and a stronger Poland keeps Russian strength pinned in the West.)
China would probably nibble a bit, perhaps Persia. But it would likely remain otherwise decentralized and tribal until the Russians get their act together.
Certainly by the 18th century there's no way, barring the collapse of the Russian state, that Siberia would still be free.
You can weaken Russia's grip but you cannot shake it free.