The ancient world's experience of time and temporal consciousness is genuinely different from the modern experience in ways that historical study can partly reconstruct. The absence of mechanical clocks meant that time was approximate, solar, and seasonal rather than precise and abstract.
Romans divided the day into 12 hours from sunrise to sunset — meaning the length of an 'hour' varied by season and by latitude. A summer hour in Rome was about 75 modern minutes; a winter hour was about 45. Coordination across distances was impossible at this level of precision. The sundial (for day) and the water clock (for night and cloudy conditions) gave approximate rather than exact time.
The year's structure was religious and agricultural: the calendar marked religious festivals, agricultural operations, and auspicious and inauspicious days rather than abstract weeks. The Roman calendar before Caesar had become so politically manipulated — pontifices could add or remove days for political purposes — that it was months out of alignment with the solar year.
The historical sense of deep time was available to ancient thinkers but calibrated very differently from modern understanding. The Mesopotamian king lists stretched back tens of thousands of years. Egyptian chronology was organized around dynasties going back to the mythological first king. The Greek and Roman historical tradition worked with roughly 700 years of reliable history and then mythology beyond that. The modern concept of geological time — billions of years — was simply unavailable to ancient minds.