The problem is that chronology tends to work not via long unbroken records, but by chaining events from different civilizations using different calendars.
For example, the Athenian statesman Pericles died in 429 BC. So far as I know, historians are pretty confident about that date. Why is that? Well, I’m far from expert on this period, but I imagine that there are documents stating that Pericles died when so-and-so was archon of Athens.
Now, it’s not as if we have a list of 2,500 archons stretching from Pericles to today. At some point the office ceased to exist. But at some later date we have documentation that so-and-so was archon of Athens while someone else was consul at Rome. Then, we have a list of the Roman consuls that eventually links up with the ab urbe condita numbering scheme. Later events synchronize ab urbe condita with other ancient systems of reckoning, such as the Seleucid and Dionysian eras. Finally, the documents of the early Christian church, which labored diligently to construct accurate Easter tables, show how these other ancient systems convert to our modern year-numbering scheme dating back to the alleged birth of Christ.
So a chain of reasoning allows us to date events from ancient Greece, not an unbroken record of events in Greece itself. There may be isolated events from later Greek history that we can’t date, simply because they were recorded on a schema that we can’t chain to the present.
Likewise in China–acording to Wikipedia, the Zhou Chinese began dating documents from the regnal year of their emperor in 841 BC. China wasn’t unified at that time, nor on many occasions since. No dynasty, obviously, ruled continuously during that time span, and at any given time parts of China might be suffering from anarchy and civil disorder. However, my (imperfect) understanding is that at least one dynasty, in one part of China, was keeping accurate enough records throughout the subsequent centuries to allow regnal dates to be “chained” backward to the first millennium BC with a pretty high degree of confidence.
What about ancient Egypt? We have fairly accurate dates in Egypt back to about 3,000 BC, but it’s hard to argue that these are “continuous”. Documents at the time were dated to pharaonic reigns, and there were periods of civil disorder where our knowledge of the pharoahs and the length of their reigns is pretty spotty. (Or, at least our knowledge was spotty; I don’t pretend to keep up with Egyptology.) Accurate dating from the earliest dynasties depends at least partly on astronomy, as the quirks of the Sothic cycle and fortuitous records of eclipses help to establish absolute chronology.
I don’t know if all that helps, but it’s an ambiguous question.