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For rock material, we generally consider it's age as when it solidifies. Most meteorites are this age because they came from a supernova explosion of our sun at the end of its prior generation. This ejected most all elemental material lager than Hydrogen in our solar system. These elements were fused in that prior sun and ejected during the explosion. What didn't coalesce into a larger body (e.g. a planet) froze into space dust and small asteroids, some of which falls to earth.
So, the amalgam that makes up the rock is 4.5Ga (giga anum), the minerals within are about the same. However, the elements that made up the stone were made long before in inside the prior sun. Now how long the subatomic particles have been around is a question for someone else.
I know how it all works, but it's just somewhat weird. Some of the posts in this thread are about houses, but they are made up of other things, sometimes older, like bricks. They don't consider those though. If the OP here used his meteorite as a piece of his house, would he no longer consider it the oldest thing he owns? It's a ship of Theseus. Why does it change when it's part of something else? (Rhetorical question.)