There are absolutely genealogical records of that time period, particularly from the Byzantine Empire

There obviously are records of most European nobility, and of course China has records... but the Eastern Roman/Byzantine Empire would be the source for voluminous ones of more than just royal lineages. Romans loved recording minutia and it would be rather inconceivable to fabricate that quantity of recorded history.

The concept of "phantom time" comes from not understanding the "dark ages" in Western Europe. There was still the rest of the world going on and the monastic culture was still traveling to and from and communicating with Greece and Byzantium. Maybe we are off a few months to a year or two, not more.

There are absolutely genealogical records of that time period, particularly from the Byzantine Empire

There obviously are records of most European nobility, and of course China has records... but the Eastern Roman/Byzantine Empire would be the source for voluminous ones of more than just royal lineages. Romans loved recording minutia and it would be rather inconceivable to fabricate that quantity of recorded history.