https://www.newyorker.com/magazine/2018/11/26/do-proteins-ho...

Under the right conditions, proteins can survive for millions of years. In recent years, proteomic studies of art works and archeological remains have yielded biological information of startling clarity, revealing gossamer-thin layers of fish glue on seventeenth-century religious sculptures and identifying children’s milk teeth from pits of previously unrecognizable Neolithic bones.

You’d probably like this short story which is about exactly what you’re describing: https://www.lesswrong.com/posts/5wMcKNAwB6X4mp9og/that-alien...

from a random page on the web

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Mendeleev realized that the physical and chemical properties of elements were related to their atomic mass in a 'periodic' way, and arranged them so that groups of elements with similar properties fell into vertical columns in his table.

Gaps and predictions Sometimes this method of arranging elements meant there were gaps in his horizontal rows or 'periods'. But instead of seeing this as a problem, Mendeleev thought it simply meant that the elements which belonged in the gaps had not yet been discovered. He was also able to work out the atomic mass of the missing elements, and so predict their properties. And when they were discovered, Mendeleev turned out to be right. For example, he predicted the properties of an undiscovered element that should fit below aluminum in his table. When this element, called gallium, was discovered in 1875 its properties were found to be close to Mendeleev's predictions. Two other predicted elements were later discovered, lending further credit to Mendeleev's table.

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Or purely mathematical intuition.