I've been wondering this due to historical inaccuracies in the Bible, like the entirety of the judges period. So, which written accoumts can we take pretty much at face value? I'd like to have some of these questions answered. At least I believe Roman texts seem to be accurate, even to modern standards, but not so for Greeks (even now, it's uncertain Socrates was a real person), which still seem better than what came before. How long did it take for Europe to recover that level of reliability after the Middle ages? Also, how reliable are non Western sources? I'm not really sure about India, but at least post Spring and Autumn period China kept plenty of records from state officials, so I'd say they're reasonably accurate.
The issue of "reliability" or "objectivity" is a central concern of historiography, but the history profession doesn't see things quite the way that non-specialists do, and certainly doesn't attempt to divide sources into piles of "reliable" and "biased" materials; nor is it generally accepted that it is possible to arrange sources on a timeline and see them get more or less "reliable" en masse across a variety of periods.
There is always more to say, but, while you're waiting for fresh responses to your question, you might like to review a couple of earlier answers that examine this thorny topic.
I explain that all sources are biased, and discuss why this is a good thing here, and u/Georgy_K_Zhukov talks a bit further about the ways in which non-specialists misperceive the issue of reliability here.
Finally, it's worth thinking a bit further about Chinese historiography, which very definitely cannot be considered "reliable" simply because it was produced by experienced scholars working with access to state archives. This is because it was always produced with some very specific purposes in mind. I talk about some of the problems Chinese historical writing can cause us in earlier posts here, specifically in relation to Empress Wu, and here in the case of Wang Mang.