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One technique is radiocarbon dating:

https://en.wikipedia.org/wiki/Radiocarbon_dating

EDIT: For artefacts made entirely out of stone, you can date objects in the sediment around them to get an approximation.

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But that only works for organic material. Not stone.

The article says there were traces of pigment that could be dated. There are other techniques related to the layers of sediment or other clues. I think with a site like this they don't need to date every object. If they can gather enough data points they know when the site was in use. It's technically possible that the statue stone is older and was brought to the site and we might never know, but it's just highly unlikely.

I think the "highly unlikely" part is pure speculation.

If the stone in TFA gets buried when _our_ civilization collapses, the stone would now probably date to 2020 AD instead of whatever it should have been.

There is organic matter buried in and around the site that can be used to date the point at which it was filled in.

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