Is there a standard data science epistemology?
Interesting question.

The way I see it, the justification comes from both mathematics and experimental science.

If you suggest a new algorithm, you should state your assumptions and provide a proof, just like in math. However, you should also demonstrate it on real data, showing that your assumptions are reasonable and that your algorithm can deliver value.

If you suggest a model, you should justify it based on its performance on the observations, just like in experimental sciences. This is true no matter how did you derive the model. However, examining the model logic itself and the way it was derived will help to gain confidence in it and trace where it needs modification.