You would need
1) Conversion of Yuehzhi, I mean a total conversion and not being, as many nomad-issued empires, hosting different religions at the same time.
2) Nomad/Steppe empires doesn't unify people they encounter, not really : at best they are able to integrate them into sort of confederation as Huns were able to integrate Goths, without crushing their organisation and having a real influence on their "way of life" (for lack of a better world). Or, speaking of Sarmates, being under the thumb of Goths didn't prevented them to eventually switch against them.
So, not even talking how they would be able to crush everyone in sight (let's admit they do), such domination would end with at best 10% of actually Yuhezi people inside (with them being only partially Buddhist if they are no entierly converted before), the remaining being or Christianized, or pagans.
Admittedly, a good start would be a Kuchan Empire that doesn't fall in the III century, and able to eventually conquer Persia and Anatolia (with No Islam, it would make three PoDs : Weaker Sassanids and Stronger Kuchan), being the only real way, in my opinion, to have to nerf Volga/Caspian trade road and to benefit to the connection made with Silk Road.
And even all of that isn't a given : to be sure it would lead to a Irano-Kuchan continuum prevalent, you'll need also a much weaker ERE than OTL that, given the "No Islam" part wouldn't be a piece of cake.
3) Again "there's a PoD, so anything could happen for no given reason"-AH is bad, lazy AH*. Good AH is when you explain why and how it's changing, would it be only in passing
* I'm talking about how is done AH on the board, actually. Obviously, AH being more a background for a novel/comics etc. doesn't have (and probably couldn't) to be that precise or plausible.
Let's see the map, shall we?
As you can see there's two roads : Volga/Caspian, Volga/Dniepr. Eventually, to make the road benefitting to a western Buddhist continuum, an Irano-Kuchan, you have to prevent the biggest trade center in the region, aka Constantinople, to be such. That is, with "No Islam", that's going to be an hard job (hell, it was already with "With Islam" reality).
Furthermore, to have a *Russia* going Budhist, and not nerfed Bulgaria, you have to divert the road or to have a western, now secondary road dominated by Buddhists traders.
See, Russia is basically that at first : a state put in the middle of a trade road, an highway shop turning independent.
No trade road from Novgorod to Black Sea, no Russia : simple as that.
So eventually and to resume , there's the challenge :
1) Make Kuchans stronger, eventually able to takeover Sassanid and form an Irano-Buddhist continuum while they didn't really suceeded to impose Buddhism to N-W India as totally prevalent (even if they DID make it influential : you "just" have to make it more missionary; converting driven, maybe altering
mahanya Buddhism to make it such)
2) Having an ERE strong enough to be a commercial center and devellop the OTL Russian trade road (without Islam, it would be a piece of cake, but could happening later TOTL), but weak enough to be challenged by Irano-Kushan at the point they would be unable to dominate it eventually (and that would be a bit contradictory)
It can be a very, very interesting TL, but it would be an hard one to put in place : without really convicing explanations for both, and critically 2), I place my bet on Christian Russia eventually.