Well you're in luck, I'm a history major and very informed on the ancient world era. The fact of the matter is, is that the allure of money has made people do crazy things. Merchants would travel though unexplored areas of the world, crossing over mountains and through jungles, trying to get to distant lands and bring back invaluable trade goods. The Middle East is still a part of Asia, even though we never really see it that way, but as more of a subcontinent.
If you read the Old Testament in the Bible, various books give detailed descriptions of trade goods that were imported or exported from various kingdoms and nations, and where the finest products came from, such as the best linen, the finest purple or scarlet silk, the best gold or silver, gems, iron, or bronze, as well as various woods for making different kinds of decor. Also, there is a special jewel called lapis lazuli which is found only in the northern mountains of Afghanistan, and this stone was imported by merchants all the way to Mesopotamia, during the reign of the Sumerian city-states from 2500-2000 B.C.
Also, another important factor was the life and religion of Siddhartha Budda. Since he was an Indian prince, and since his religion had many followers, after his death, missionaries went into different parts of Asia spreading the new ideals of Buddhism, which was around the middle 400's B.C. Buddhism reached Persia perhaps 100 years before Alexander, and so with the new religion came people from India and various different trade goods, as well as new ideas. Not to mention a good portion of west India was conquered by Persia during this time.
The problem lies in that beyond the advanced realms of India lay the uncharted and mostly tribal kingdoms of the Khmer, which was Thailand, Malaysia, Cambodia, Laos, and Burma. In order to get through this land, you needed a guide, most likely, and someone who could speak the language, as there was always the chance you would be murdered for being an outsider. For a Greek, it would be impossible. But for a Persian who has Indian vassals, it could be accomplished. This would also require several translators to get by these lands, or guides. And lastly, China. To get to the heart of China would probably require one or two more translators, unless the Chinese were familiar with Khmer or Indian dialects. Whether or not China was united makes little difference, because trade routes were still used and the Chinese still encouraged foreign trade.
The more brave route would be to go around the Himalayas, through Tibet, and go around the Gobi desert, most likely underneath it in Tibet, and head east for China. Although it would have less people and less "jungle danger" from poisonous snakes and the like, the climate would still be very cold, and probably lots of mountains to cross. However, like I said before, the allure of money makes people do crazy things, and just as explorers in Europe tried to find the bottom of Africa, and even tried to chart the Nile, it is extremely unlikely to say that no one tried to reach China and come back with riches. It is also extremely unlikely to say that no one succeeded, either. In Alexander's time, the silk road would be much less dangerous than it would be before his time, but not impossible.