Yes, the Axis have to move fast if their goal is to take down Russia. The problem is that they aren’t capable of moving fast. Leningrad can be fortified to prevent a naval G2 attack and a land G2 attack is going to be extremely difficult. On turn 3 Russia can just move their forces out. That’s part of the issue; If Russia always keeps its forces one move away from Germany with an infantry in between, they can amass a huge force. Germany is stuck moving one space at a time. Even if you send Japan and Italy against Russia they can’t move very quickly. Italy can’t get to Iraq until I2, build an IC until I3, build units until I4, and if Britain liberated the persian extra units and merged them with just a few Russian units in North Persia, Italy might not be able to attack Russia until late game. The same issue occurs with Japan, even if Japan invades Russia and tries to take up as much money as possible, the Russian stack can move one space away all game long. Sure, Russia loses some money, but Japan is going to struggle to effectively fight anyone else.
Bottom line, I’ve played multiple games as the Soviet Union where I didn’t let anyone attack my units except an infantry I left as a road block. Even when Japan invades Russia turn one/two and tries to keep pushing, it still didn’t make much difference because they can only take a territory a turn. So when Germany finally reaches Moscow, almost every single unit I’ve built as Russia is there defending my capital. Sure, if time weren’t a factor, it’s a bad strategy, but I know that the Allies are going to be landing in force by turn 5 or so, so the Axis is not able to deal with the Allied pressure and overcome a huge Moscow stack.