Great Perm was my first run when Third Rome dropped:
https://www.reddit.com/r/eu4/comments/6igl0q/its_the_permian_explosion/?st=J7R75VSV&sh=2667941b. Truly a test of patience, and it's the one run that I don't really have a strategy for. Novgorod usually is invalid as he almost always gets declared on immediately, Lithuania isn't good enough on his own and the hordes never even came close to wanting to support independence. I really only succeeded when Lithuania took a local noble, allied Poland and the Kalmar Union and called them all in against Muscovy, so I declared on my own. Muscovy fortunately didn't come for me, so I managed to siege down Nizhny Novgorod + a few other provinces and peace out for independence and 6 provinces. Then, expanded into a weak Uzbek and Kazan, allied Lithuania and Muscovy was no longer a problem from then on.
Actually, I may have an experimental strategy. Rush exploration ideas and explore terra incognita down to Ming, who will support your independence after some improving relations as his starting ruler is usually Naive Enthusiast. You just need to wait until the "cannot reach Muscovy" modifier mysteriously goes away after a few years. This will make your liberty desire skyrocket and prevent you from ever getting annexed. Then, you could sit back and colonise Siberia until around 1590, which by messing around with the different start dates I was able to determine as the approximate time that Ming discovers the Russian region (attitude towards Muscovy/Russia changes from unknown to neutral), then declare independence and let Ming do the work for you. If you declare before Ming discovers the region he won't help you at all because his troops can't get there. However, you'll still be in a big pinch as Muscovy should have formed Russia by this point and may have eaten all the hordes leaving you no space to expand, and you may not make it in time to get the achievement.
