The Grand Saros Canon, Almagest, and Ch'un-ch'iu bear out a timeline reaching back to the 8th century BC. So does the Babylonian chronology stitched together by historians.
Some researchers are chary of the Late Babylonian calendar and have misgivings about extending the time line beyond 400 BC. But Ptolemy certainly believed absolute dating was viable back to the 8th century BC. Ditto for the Hellenistic Babylonians who produced the Grand Saros and the Chinese of the 1st century AD who chiseled the Ch'un-ch'iu into large stone slabs.
Historians have not come up with a convincing explanation of the revolution in astronomical understanding that made a time piece out of the apparent confusion of celestial events. The default explanation is pretty much the same as the one advanced by Ptolemy, i.e. the novice star gazers were more interested in omens than astronomy and thus Babylonian observatons prior to the 8th century had not been preserved.
Still, if Babylonian priests were inclined to read the future from livers rather than stars, what impelled them to alter their traditional ways?
Possibly King Nabonassar instigated the 8th century revolution by inaugurating the era that came to bear his name. Many facts point to his reign as the beginning of an epoch, and hence Nabonassar might be the innovator who established the first era long before the Seleucids. However, not a shard has been found of this hypothetical era. The evidence in hand indicates the Babylonians dated by means of regnal years.
The year 747 BC, or a date somewhat later in the 8th century, appears to mark the limit of secure astronomical dating.
To be sure, historians of all periods look to astronomy to bolster their historical reconstructions. They also seek corroboration from radiocarbon dating, tree rings, and other techniques. But their work rests on a bedrock of king, eponym and other lists, archeological strata and the sequences derived from them, in short, on traditional historical techniques. Only in the Ancient Near East and its periphery, and only back to the year 747 BC has astronomy taken the lead in building an ancient chronology.