The proof is very simple. But for the answer you must ask first: what is time? And that is a bit more difficult.
In special relativity (Minkowski diagrams) we currently distinguish between the observed time and the proper time.
Observed time is only relative to each observer, but it has the advantage that we can build up a time axis, permitting to say that two events are happening simultaneously or not. But another observer moving at another relative velocity will have another perception - simultaneity is relative.
Proper time is absolute. Proper time is the time which is measured by a clock. If you feel that you are getting older it's your inner clock which is telling you so.
The proper time of a thing is the same for each observer. Your twin brother coming back from a travel near light speed will be younger than you (due to the so-called twin paradox) but nevertheless he will estimate your proper age in the same way as people do who remained on Earth, and in the same way as yourself. If you are 60 and you are looking like 60 everybody will agree that you are 60 years old. It's your proper time.
The main error committed with respect to time is to think that spacetime provides the answer of what time is. Within Minkowski spacetime, time is a fourth dimension. Minkowski spacetime provides a relation between space and time. Many physical questions may be resolved by spacetime. But for the question what time is Minkowski spacetime cannot help because Minkowski spacetime is relative.
As a consequence, time is reduced to proper time, the proper time of any clock. And you will understand the physical definition of time: time is what is measured by clocks. Nothing more and nothing less. Have a look at your watch, see how time is passing. Feel yourself getting older, time is not exempting you. There is no need for additional proof that time exists.