> All the texts that mention the Hittites post-date the fall of the empire based out of Ḫattuša by centuries

I don't see how this would invalidate the legitimacy of the documentation. The Hittites were large enough to be visible to contemporary historians and scriptures were used for information preserval. Even if our knowledge was only preserved through written documents, we'd have a good grasp of history 300 years ago, especially of major societies. People weren't primitive back then, they even had state archives with historical records which the Bible mentions in a few places for further reading.