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Any kind of object clearly restricted to a specific point in the geologic column would do just fine.
Radiometric dating would later confirm the relative ages of the strata and tie them to absolute dates.The depth of burial, itself, has little to do with our mystery.In some parts of the world the Cretaceous is found deeper than is the Cambrian in other parts of the world.Your chances are 6.2 billion to one of getting the right order for all thirteen.And, when you consider that each period can also be divided into "upper, middle, and lower," the odds of arranging them in the correct order by pure chance become astronomical. It has correctly placed the Cambrian between the Precambrian and the Ordovician, the Ordovician between the Cambrian and the Silurian, the Silurian between the Ordovician and the Devonian, and so forth.
(Far from being a rubber stamp, radiometric dating would go on to revolutionize our understanding of the Precambrian.) Thus, it became possible to date strata directly from index fossils.