Alexander did it marching over land that was fertile (mostly). His army could a) live off the land, b) requisition stuff from satrapies as they took each in turn...
But China had some other advantages which Alexander the Great didn't have:
a) the Chinese Empire(s) had the greatest resources to support the invasion and the conquest in the Central Asia and Iran. That's why the Chinese army doesn't have to live off the land - using their excellent logistics they are able to build the road(s) beforehand and a chain of fortresses. And that was sometimes in place and even more - the Great Wall covered part of the road:

So before the invasion China needs to store the food supplies in those fortresses so the Grand Army of invasion might have less train of supplies with it. As it is seen from the map, the hardest part (through mountains) is already taken.
After that goes pretty fertile agricultural lands where in addition to the supplies from China it is possible to live off the land.
And Alexander the Great had the minimal pool of human resources, Macedonia was actually a little country with a small population scattered over the mountains mostly; the Greeks were rebellious, the locals even more so.
China probably had the biggest population on the planet.
b) The Chinese armies might count on the requisition stuff from the regions they're gonna to conquer each in turn, those were pretty rich lands.
But that's not the main incentive for the Chinese conquest; the idea of invasion is to cut off the middleman on the "Silk Road" - every 100 miles of the occupied Silk Road gives China 'a ton of gold per year' (figuratively speaking of course) - that is another advantage, which Alexander didn't have.
-------------------------------
But the point is China doesn't need this 'conquest of Central Asia and Persia'.
I mean controlling Silk Road is good, cut the middleman is fine.
But Silk Road is not necessity for China.
- If one day all the Silk Roads shut down what happens to China?
- Nothing. I mean, tons of silk stays in China, which is good. Well, China won't get some gold from West, but the point is the Chinese economy may function pretty well on paper and bronze/copper currency, no problem whatsoever. China has everything it needs.
The other problem with China expanding West is that this expansion dramatically extends the border with the Great Eurasian Steppe (from the North).
And every Chinese knows that it is the North where the greatest danger to China lies - the steppe nomadic tribes are waiting for their chance, when China is weakened, and the nomads unite and strike the deadly blow.
So the
real longtime interests of China is to keep the Northern border as short as possible, which means no "Go West" strategy.
There are plenty of other ways to expand for China and the resources taken there might be used to strengthen the existing (preferably short) Northern border.