The simple answer is that conventional civilization only came to be in fertile, food-secure areas where untrained proto-agriculturists could congregate in large settlements. All the cradles of civilization have all been continuously settled for thousands of years, people just like living near food.

But if you are asking why China has been a continuous state for 3500 years, your belief is unfounded.

The simple answer here is that "China" just isn't a 3500 year old entity, as "Italy" is not 2500 years old, and "Egypt" is not 5000 years old. The geographical locations of these countries have been inhabitated for all those years (And more), but their first cultures are rather unrecognizable when compared to their modern and pre-modern descendants.

The written records of 1500BC China are oracle bones from the Shang dynasty. These are not really records per se, the Shang wrote questions to their ancestors on the bones, shattered them with heat, and then interpreted the pieces. We can reconstruct a timeline of Shang rulers, because the reigning Shang lords would often address questions to their predecessors, but they were not written as histories.

Besides what we can infer from the oracle bones, we don't know much more about the Shang. They most likely didn't have any conception of "China", much of what we would now consider the heartland of China were lands full of barbarians to the Shang.

This is not to discredit Chinese history of course, since it's true for all of the world's countries. The earliest civilizations of the Fertile Crescent were similarly alien to their direct successors, for example.