In 329 BC, Alexander reached the Ferghana Valley. From there, it’s quite feasible to cross the Pamirs and march on Kashgar. Crossing the Pamirs would be an impressive feat — akin to Hannibal crossing the Alps — but not impossible.
The Tarim Basin city-states were militarily weak and could be easily conquered. The climate was much wetter then, supporting a larger population to feed a Macedonian army.
The real challenge for Alexander’s mainly infantry-based force would be crossing the long, sparsely populated, arid steppe and the Gobi Desert along the Hexi Corridor to reach the Yellow River, where significant settlements could be plundered.
If we assume Alexander could somehow solve the logistics of supplying his army through the Gobi, they would eventually meet the Qin state — already a formidable power. The Qin heartland lay in the Wei River Valley, also known as “the land within four narrow mountain passes.” Gaining entry required overcoming the crucial western pass of Xiao or Shan, a difficult task.
However, in 328 BC, the bulk of the Qin army was east of the Yellow River attacking the Wei state. If Alexander could force-march his troops from the Ferghana Valley to the Qin border within a year, and secure allies among Qin’s western neighbours, there was still a chance to break through the western pass into the Qin heartland.
The real question is whether Alexander’s expeditionary force could defeat the Qin main army if it returned from the eastern front. Qin could field a much larger army. In 331 BC, Qin forces reportedly cut off at least 45,000 Wei heads in a single battle, according to Wei records.
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Could Alexander the Great conquer China?
Carl Zha considers whether Alexander’s army, after crossing Central Asia, could have breached Qin defences in 4th century BC China.
If Alexander is able to force march his troops from Ferghana valley to Qin border in 1 year, find native allies among Qin western neighbours, there's still a chance to break thru the western pass into Qin heartland.