A lot of Russian contracts were made with the U.S for weapons, like the famous Winchester 1895, where ~33,000 went to Russian service. Alot of work being done before war, so these trade links existed. If those contracts go out earlier, and with more of a focus on buying American guns rather than having them produced in the Russian Empire (how this works with U.S law / neutrality policy I'm not sure) and ramping up American production, this could alleviate some supply issues they had early on. As another user pointed out, taking things into the hands of more efficient local war councils/manufacturing earlier on could do wonders for Imperial logistics.
I think one issue which caused far more dissent than was worth were the repressive measures against internal "enemy nations" which caused food issues and riots in the interior of the Empire far from the front. Refugees are probably unavoidable, but deportations are just adding fuel to the fire.
Frankly, I don't know how a "Russian victory" is possible unless they sweep the Central Powers militarily fairly rapidly and easily for the Russians to keep their Empire. "Russia" was a multinational Empire as much as the Ottomans or Austria-Hungary. If Galicia and parts of Silesia and/or the corridor is annexed to the Empire, more Poles and Ukrainians will only cause more and more troubles for an Empire which is running on fumes. Once Pilsudski's Polish legions and the Ukrainian Sich Riflemen take up arms, it becomes clear that Russia has major nationality problems that probably will have lasting repressions. America does not want to be on the side of Russia and their repressive Empire. It's embarrassing enough for the Entente as it was, if they end up annexing Polish and Ukrainian territory, it will cause internal friction with the Entente and I can see Britain being obtuse about it, worried about Russia as it traditionally is.
Can Russia "win"? Probably. Can they win and maintain their pre-war system? I don't think so.