Classical chronology was never an exact science.
During the Classical period, infamously, almost every Greek city had its own dating system, just as it had its own calendar and laws. In Athens, for example, an official called the eponymous archon gave his name to the year. At Sparta, the year was named after one of the ephors. At Argos, the priestess of Hera had that honor.
The dizzying array of dating conventions created enormous headaches for ancient Greek historians, who had to either pick a single dating system, like the Athenian archon lists, or craft cumbersome synchronisms. It was possible, however, to build long-term chronologies. Perhaps the most famous example is the Parian Marble, an inscribed chronicle recording events from 1582 to 298 BC.
The best-known Greek attempt at a systematic chronology was the Olympiad system, pioneered by the historian Timaeus and systematized by the polymath Eratosthenes in the third century BC. This system dated events in relation to the Olympic Games, which had been held every four years since – by Eratosthenes’ calculation – our 776 BC. An event that took place in 480 BC was thus in the year of the 75th Olympiad. The Olympiad system was useful for historians, but it never became standard like the modern AD/CE system – and it seems to have never been referenced in daily life.
Like the Greeks, the Romans typically dated years by annual magistrates – in their case, the two ordinary consuls, who took office – by the imperial era – on January 1. Consular dating remained standard throughout Roman history. Roman scholars, however, sometimes referenced what we call “ab urbe condita” dates, counting the years since the foundation of Rome. There was never a definitive date (then as now, historians disagreed about such things), but most scholars thought that Rome had been founded around 750 BC. The date calculated by the polymath Varro, 753 BC, was the most widely accepted.
Like the Olympiad system, however, dating from the foundation of Rome was a convention used more or less exclusively by historians.
In other words, there really wasn't a clear conception of "antiquity" in antiquity, since their conception of the past was less neatly defined than ours. (And our conception of the classical past, it should be noted, is exceptionally - perhaps overly - neat, conditioned by the AD system and by the Renaissance obsession with antiquity, both of which have shaped how we tend to teach ancient history.)
If there was a division in ancient conceptions of the past, it was marked by the Trojan War. Myth and history were never neatly disarticulated in the classical imagination, but the Trojan War marked the point of separation between a past that was (thought to be) known and a past that was acknowledged as all but unknown, save through the traditional narratives we call the myths. Most ancient authors seem to have believed that Hercules and Jason had indeed existed (whatever their thoughts about the received myths surrounding these heroes). But they imagined them, or at least tended to write about them, in different terms from such "historical" figures as Themistocles and Xerxes.
The antiquity of antiquity, in short, was the world of myth.
While looking for an answer for myself I found this old thread with an answer from u/AbouBenAdhem/