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.
Many other indicators are commonly present, including ones that can even tell you the angle of the depositional surface at the time ("geopetal structures"), "assuming" that gravity was "down" at the time, which isn't much of an assumption :-).
In more complicated situations, like in a mountain belt, there are often faults, folds, and other structural complications that have deformed and "chopped up" the original stratigraphy.
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.
To get to that point, there is also a historical discussion and description of non-radiometric dating methods.The layers of rock are known as "strata", and the study of their succession is known as "stratigraphy".Fundamental to stratigraphy are a set of simple principles, based on elementary geometry, empirical observation of the way these rocks are deposited today, and gravity.Geochronologists do not claim that radiometric dating is foolproof (no scientific method is), but it does work reliably for most samples.It is these highly consistent and reliable samples, rather than the tricky ones, that have to be falsified for "young Earth" theories to have any scientific plausibility, not to mention the need to falsify huge amounts of evidence from other techniques.