time is a function of the universe and therefore can only exist within the universe; when the universe begins, time, however you define it, begins. when the universe ends, time ends.
Cyclical time is not religious, it is astronomical. it has religious overtones because the guys with the brains were often clerics; also, it has often been the only authority sufficiently recognised to enforce changes to calendars as required.
a year is defined as the full circuit of the earth around the sun; a day is the time taken for the earth to fully rotate on its own axis. the two do not match evenly requiring adjustments to ensure that midnight in 10000 does not fall in the middle of the day- hence calendars.
the role of the modern clock is not religious either; it is industrial. the first clocks did not have hands but simply chimed the hours. for the benefit of both workers and employers it evened out the work day- which had been traditionally fixed at dawn to dusk. the clock meant that instead of working 18hours in summer and 6hours in winter, with all the personal, familial and work impacts, you worked a standard day throughout the year.