Dating different fossil technique
This orientation is not an assumption, because in virtually all situations, it is also possible to determine the original "way up" in the stratigraphic succession from "way up indicators".
For example, wave ripples have their pointed crests on the "up" side, and more rounded troughs on the "down" side.
The simplest situation for a geologist is a "layer cake" succession of sedimentary or extrusive igneous rock units arranged in nearly horizontal layers.
In such a situation, the "principle of superposition" is easily applied, and the strata towards the bottom are older, those towards the top are younger.
Much of the Earth's geology consists of successional layers of different rock types, piled one on top of another.
The most common rocks observed in this form are sedimentary rocks (derived from what were formerly sediments), and extrusive igneous rocks (e.g., lavas, volcanic ash, and other formerly molten rocks extruded onto the Earth's surface).
Most of these principles were formally proposed by Nicolaus Steno (Niels Steensen, Danish), in 1669, although some have an even older heritage that extends as far back as the authors of the Bible.
Cave deposits also often have distinctive structures of their own (e.g., spelothems like stalactites and stalagmites), so it is not likely that someone could mistake them for a successional sequence of rock units. Each of them is a testable hypothesis about the relationships between rock units and their characteristics.
They are applied by geologists in the same sense that a "null hypothesis" is in statistics -- not necessarily correct, just testable.
In the last 200 or more years of their application, they are valid, but geologists do not assume they are.
For example, the principle of superposition is based, fundamentally, on gravity.
In order for a layer of material to be deposited, something has to be beneath it to support it.