These "objects which sequentially (concatenationally)  impinge upon another (and thus are themselves impinged upon) that exist" appear to have an ordering, a sequence, according to your statement.  Any ordered set can be subjected to a high level of measurement and comparison (a ratio level in this case). So, by your own definition we can discover the relations within and between sets.  We can do science.

Science shows that there are at least two sorts of "time": dimensional time and the time of change.  "Dimensional time" is related to the spatial measurements of high speed objects and allows us to calculate the exact values of magnetic fields, kinetic energy, gravity etc.  You may not agree that this exists, if so, please suggest an experiment to demonstrate this assertion.  Science also points to a time that is related to the evolution of physical systems, this has a particular direction and is related to thermodynamics and quantum theory.