I have no idea what the Russians believe or not about stopping a MIRV attack. Only if the Russians were to attack us, we would need a lead time to deploy any putative defenses - they do not, since there defenses are already deployed.
Further, they are willing to take large casualties, we are not; they have elaborate shelter systems for the populace and full scale underground cities, we have neither.
Belief really does not enter into it. Preparation does.
Will their SA systems actually be able to stop a MIRV attack, will either side’s warheads reliablly detonate - are questions which can only be answered by putting the questions to the test.
We certainly have no SA system to stop a MIRV attack, they may have. Something is better than nothing - we have nothing ... AFAIK.
The Russians freaked out when we announced deployment of defensive missiles in Western and Central Europe. Much of their current and planned ICBM force consists of liquid-fueled, silo-based missiles. These are just very expensive sitting ducks. I don’t lose any sleep over Russia’s current nuclear capabilities. Many of us did in the 1970s, for no reason as it turned out, because we vastly overestimated their military strength and technology.