this might all be MOOT now, but i did this anyway

i'm going to do a quick sanity check, to see if this is even in the ballpark, so making a few assumptions, about the Kinzhal. lets just say it has the same mass as an AGM-129 3500lbs and lets take them at their word, that it's doing mach 10 (maybe it's going faster, maybe it's going slower)

and also.. just ignoring any warhead it may have on board

converting everything to metric

3500lbs = 1588 kg, lets just say 1600kg and mach 10,,. at sea level 3313 m/s, lets just call it 3300 m/s

the kinetic energy . KE = (1/2) 1600kg * 3300^2(m/s) or KE = 8,712,000,000 Joules that's 8.712 Gigajoules and that's without any warhead going off

so using another table/calculator i found here https://www.justintools.com/unit-conversion/energy.php?k1=joules&k2=atomic-bomb-[nuclear-weapon]

I can convert your glide bomb with a 1500lb warhead (680kg) to giga joules I used Kilograms of TNT to gigajoules as the conversion 680 Kilograms of TNT work out to 2.84512 Gigajoules

8.712>2.84512

so assuming.. that warhead weight is equivalent to KG of TNT, , and assuming that a 1500lb(warhead size) glide bomb could penetrate 400 feet of rock along with layers of steel, than, the Kinzhal missle has more than enough energy to penetrate (completely disregarding any warhead it would have).

that being said, i'm not fully confident of those assumptions(you would likely know better than me),., but it makes for an interesting sanity check, and the results are a definite maybe.