This question, and the answers thereto, make it seem like there's something unusual about time. There isn't.
Processes with characteristic duration are the set of all repeating or repeatable processes whose periods (or the average of a large number of periods) are expressible as a fixed ratio of any other process in the set. A duration is a number times one of those periods. For consistency's sake, it's good to pick just one process that deviates as little as possible over the fewest possible iterations, in its ratio to the average number of iterations of all other processes in the set. We can use that as a basis value, which is where we get the current SI definition of a second in terms of the transition frequency of Cs.
Processes with characteristic length are the set of all repeating, long-lasting, or repeatable processes whose spatial extents (or the average of a large number of extents) are expressible as a fixed ratio of any other process in the set. A length is a number times one of those spatial extents.
Processes with characteristic mass are the set of all repeating, long-lasting, or repeatable processes whose resistance to acceleration (or the average of a large number of resistances to acceleration) are expressible as a fixed ratio of any other resistance to acceleration in the set. A mass is a number times one of those resistances to acceleration.
So on for any measurable value that adds linearly. There's no ultimate basis value for any measurable quantity, just sets of processes that are found in reliable ratios with one another; among which we choose a basis that's easy to measure very precisely.
You can get at most one step away from this, if you happen to get very good at measuring some related quantity. For instance, experimentalists have gotten really good at making clocks and really good at measuring the speed of light and Planck's constant, so now we use Planck's constant ($h$ has units of $Js$), the speed of light squared (a conversion factor between $kg$ and $J$), and a clock, and declare that a kilogram is the mass of an imaginary process that makes Planck's constant have its standard value, given our definitions of $c$ and $1s$. If people were really good at measuring masses and terrible at making clocks, we'd do it the other way around, and define seconds in terms of Planck's constant, $c$, and the mass of a 1kg chunk of platinum-iridium alloy in a vault in Paris.
Every measurable characteristic can entertain the same meaningless "What if we're all in the Matrix?" style question.
How do we know the tick of the clock is always the same real ultimate divine second, and the universe doesn't just conspire to keep all the ratios the same? How do we know the meter stick is always the same real ultimate divine meter, and the universe doesn't just conspire to keep all the ratios the same? How do we know the kilogram is always the same real ultimate divine kilogram, and the universe doesn't just conspire to keep all the ratios the same? How do we know the electron charge and Boltzmann constant aren't constantly in flux? What if we're all brains in jars in a holographic simulation of the matrix on a computer in a computer in a computer in a universe created last Tuesday where God surreptitiously changes the real ultimate divine length of the meter and the speed of light every time it rains?