Let's take the situation you posit regarding time and consider an analogous situation regarding distance:
Imagine a world in which there is no clear, objective standard for measuring distance. Every tree is a different height and every branch, a different length. No two pairs of rocks are the same distance from each other. People are all different heights, with no universal length of their limbs or digits. Even something as simple as the length of a single person's hair could be radically different from one moment to the next.
In a world where distances are so chaotic, would people even form the concept of quantifying distance, much less find an agreed standard for doing so?
Of course, we don't have to imagine that world. We live in it. 840
And, therefore, we know that, yes, quantified distance is a universally-accepted concept, which has been standardized multiple times, in multiple ways. ("That's the great thing about standards - there are so many to choose from!")
Not only that, but we also know that, despite the variability in the sizes of body parts, they formed the basis of some of the earliest widespread distance-measurement systems. To this very day, one of the major units of those systems even shares the name of the body part it was based on - the foot.
"But," I can imagine you saying, "my foot is the same size from one day, or month, or year to the next. It's utterly consistent!"
Yes, that's true, but how about another widely-used "archaic" measure of distance: What good treasure map doesn't measure distance in "paces", the distance covered in a single step? How consistent is that distance? I know that the length of my pace varies from day to day, or even moment to moment, based on my mood, my energy level, the terrain, and several other factors. And, of course, one person's pace can vary greatly from another's, due to those same factors, plus differences in height, flexibility, fitness level...
The pace is far from a consistent measurement, and yet it was (and is!) still widely used to measure distance when more accurate measures are not readily available.
So, yes, given that humanity has quantified distance at least since the beginning of history (and I suspect well into pre-history, probably even before we became "human" in the modern sense) despite the lack of universal repeating distances to use as an objective base distance measurement, it is exceedingly likely that any similarly-sapient species would quantify time, even without having universal repeating intervals to use as an objective base time measurement.
Moreover, the utter necessity of having some way to specify both times and locations if one wishes to coordinate the activities of multiple entities makes me quite confident that it would be essentially impossible to develop anything remotely approximating civilization or technology without having the ability to specify both of them. You can't say "meet me at this place at this time so we can hunt together/research how to make fire/bring in the harvest/mate/launch our exploratory expedition/whatever" unless you have the concepts of both "at this place" and "at this time", as well as a means to express those concepts. 840