A statement of proving time by Einstein does not and cannot arise because time is not a provable entity or concept but a human made concept to track eventual changes in the Universal existence.
Time is relative in the sense it is relative to the events and since events are variable so time, as a reference scale, needs to be uniformed in its scale and therefore, irreversible progression of time is uniformed in its scale.
Events may be occurring in different local frames but all the events those occurred since the beginning of the Universe and the events those are occurring right now and the events those will be occurring in future all are tracked or going to be tracked in a single frame of reference in time that too in fourth dimension, having its absolute nature. Greenwich Mean Time is a slice of that universal time.
Time cannot stop at the speed of light because speed is movement (of real entities) and it does not have its influence on time (a conceptual entity), as speed is movement - this implies changing place or position - and time tracks all such eventual changes, even to convey speed of light one needs time to relate speed of photons or electromagnetic waves, and the known speed of light does not mean time has stopped with it, it is rather conveys the speed of light on the time scale, the galactic speed at the edge of the visible Universe are faster than the speed of light and that faster than light speeds are too tracked with the same scale of time.
Einstein believed in steady state of the Universe but never opined that the Universe keeps expanding, in the year 1922 Alexander Friedmann introduced the idea of an expanding universe that contained moving matter and correspondence with Einstein suggests that Einstein was unwilling to accept the idea of an evolving Universe and worked instead to modify his equations to ensure a static eternal Universe as believed from Newton's time.
The Space-time continuum as proposed by Einstein described a better explanation of gravity - as distortion in the fabric of space-time, - but this proposition by Einstein clearly appears defective to the extent that gravity cannot distort time as in continuum of space-time, as gravity may have influence on space or even on matter and energy but gravity cannot have influence on time, time will only exist within space and in the presence of eventual existence in the Universe when gravity may have influence on space, matter, energy and their eventual existence but shall have no direct influence on time.
The red-shift phenomenon, indicating expanding Universe, was not a discovery by Einstein, rather Edwin Hubble discovered that the Universe is expanding through the red-shift phenomenon and this discovery rather challenged Einstein's steady state Universe, accordingly this discovery also challenged Einstein’s theories to a considerable level.
Some of Einstein’s fictional stories about Time dilation, time travel, twin paradox and space-time etc. do not have valid scientific basis and these are even understandable to the high school level students now.
It is not Stephen Hawking who first predicted the concept of black holes, but it was Einstein who first predicted the existence of black holes. Stephen Hawking rather helped us to realize time better. His work on black holes, quantum mechanics and the origins of the universe advanced the theories of previous thinkers like Albert Einstein and Werner Heisenberg, providing the most comprehensive explanation for the behavior of the cosmos to date.
