There are a couple of difficulties with the “three age” system that archaeologists and historians have issue with when using them to discuss chronology with non-experts. The first is that some people would guess that, because they’re named after stone, bronze, and iron, these materials would somehow play a big role in human life during these periods and change them so much that we can easily identify one period and it’s human experience over another. In actuality, the three ages are far more useful for archaeological typology than they are for describing human life; while versions of this system existed prior, it was Christian Jürgensen Thomsen who invented the basics of the three age system used today to aid in typological exhibition of archaeological artifacts in the 18th century. Another issue is that all regions did not experience these ages at the same time and so any answer has to be contextualized; I can answer your question as far as southwest Asia is concerned, but my answer will not be all encompassing as a result.

To start with, the changes which separate the Bronze Age and Iron Age in the archaeology of SW Asia happened fast FOR ARCHAEOLOGY; in human experience, we are talking at least a few generations of human experience. As a result of this time span, nobody ever woke up and collectively agreed, “life is very different now, and we recognize this is a new age.” In fact, quite the opposite occurred.

When the Hittite state collapsed, for example, it does not appear to have done so catastrophically and everywhere at once; Lorenzo d’Alfonso (2020, An Age of Experimentation ) has argued that the different regions of Anatolia, in light of the political collapse of the Hittite empire, experienced different local trajectories in their attempts to fill the void that this collapse left behind. Some areas, such as north-central Anatolia, were more or less depopulated and seem not to have weathered this event well, but others, such as South Cappadocia and Northern Syria, retained a fair degree of socio-political complexity, maintaining a writing system in the form of hieroglyphic Luwian and/or cuneiform, and continuing to maintain some of the trappings of Hittite power, such as an association with the storm god Tarhunzas and the title of “LUGAL.GAL,” or “Great King.” While the empire had collapsed, and the organization of political life undoubtedly changed and some areas experienced sharp drops in population density, to many people, life doesn’t seem to have changed so drastically that they would have associated themselves as living in a fundamentally different world from their ancestors.

In this case, nobody woke up one morning and realized the Bronze Age was over; the idea of a Bronze Age didn’t even exist to them because it is a modern invention for periodization, and the period that we term the Bronze Age ended with the political collapse of some major polities which transferred a political legacy down to the polities and states of the early Iron Age. In Anatolia, hieroglyphic Luwian writing, which began as a monumental writing form in the late Bronze Age, survived with the same primarily monumental and political use down through the Iron Age (Payne 2004, Hieroglyphic Luwian), and many sites occupied in the late Bronze Age, such as Karchemish on the Middle Euphrates river, remained occupied through the Iron Age and continued to engage with the Hittite political legacy well into the 8th century BCE (Osborne 2020, The Syro-Anatolian City-States: An Iron Age Culture). While it might not exactly have been “business as usual” due to the political changes which impacted daily life, people did not see themselves as occupying a world which was changed fundamentally.