Age – the current temporal extent of an object. The age of an object could be read from a clock that had accompanied that object on its path through spacetime, its worldline.

The age of an object is clearly not the age of the basic material from which the object is made, it must be calculated from the time that the basic material was arranged into a form recognizable as the object in question.

Not only is the starting time of an age a bit uncertain, but the speed with which time passes is different for objects which experience different accelerations or gravitational fields. That is why true age is only displayed on a clock that has accompanied the object throughout its existence.

Suppose we have a helium atom.  The nucleus is composed of four baryons, two dressed up as neutrons and two dressed up as protons.  The whole assembly is held together by the strong nuclear force, one of the four fundamental forces of nature, the others being gravity, electrostatic and weak nuclear.  The baryons have existed since the Big Bang but their assembly into a helium nucleus has been a relatively recent event.  Prior to coming together in the nucleus the baryons had different relativistic histories so it would be very unlikely that they would all be the same age.