Time is real because tasks that have a beginning and an end have a duration. If time were not real there would be no reason why babies would not be immediate consequences or indefinitely postponed consequences of sexual unions. If time were not real there would be no reason not to market day planners to the deceased. If time were not real there would be no reason to get consent for medical procedures during times when patients are stressed by vexing bullet wounds.
More concretely, every finite path of existence possible to be occupied by a small material body can be assigned a proper durations in a way that changes smoothly with changes in position and path and entirely consistently with that measured by the most precise clocks. So the simplistic prediction that clocks measure elapsed "time" is entirely consistent with a self-consistent theory of space-time geometry.
However, this geometric time of finite paths is a quite different notion than the absolute time of Newton's conception. That older view of time does not share the same empirical support. So it is important to define one's terms. If one can't even define what one is talking about, what chance does one to understand another?
Having established that time is real, but particular to a choice of location and state of motion, we may establish that the best clocks are those that give the most parsimonious measurement of elapsed time. That is, a good clock makes local physics seem simple. Study of the goodness of clocks is a technical branch of metrology. Being a technical branch, it has its own special vocabulary to ensure that everyone's talking about the same thing. And having established that they are talking about the same thing, their concepts of what it means to calibrate a clock are fundamentally interconnected to a system of cross checks.
View attachment 1252
Figure A.7 — Concept diagram for part of Clause 2 around ‘calibration’ from page 69 of
JCGM 200:2012 International vocabulary of metrology - Basic and general concepts and associated terms (VIPM)
It's not an intractable chicken-and-egg situation, but a historical stepwise gradual refinement of the concept of what it is to measure a quantity and the precision at which we can reproduce such results. And such refinements are possible only because of the behavior of time (in the geometrical, associated with a particular path in space-time sense) of acting like a real thing.