Three types of clocksThe first type is given by an oscillation system like the ammoniak atomic clock (23,786 GHz). It is more or less independent of impressions from outside.
The second type measures the flight time of a signal between the ends of a cavity, realised by standing waves tuned to the hyperfine transition of hydrogen (1,42 GHz) in a maser clock.
The third type is provided by the collisions in a gas. It is not accessible technically, but rules any ageing of living or dead objects.
In the universe, the three clocks have different changes in rate, because light signals have to cross increasing intergalactic distances, and interaction rates decrease because of cooling and diluting effects of the expansion.
In the universe, type-1 time has a begin, but no end, type-2 time has a begin and an end as well, type-3 time has an end, but no begin.