No we don't, we make hypotheses and then test them. Hypotheses are based on data.
There are physics experiments being done right now where the exact hope is that existing theory has not predicted the result they produce, because then we'd have data to hypothesis something new.[1]
You are literally describing what deep learning techniques are designed to do while claiming they can't possibly do it.
[1] https://www.scientificamerican.com/article/measurement-shows...
Deep learning models are data: they are just associations between points.
Train a NN on data generated from an exponential function, and the model produced is not exponential.
Train a NN on the covid pandemic, and you will never obtain the SIR model.
AI is just associative statistical modelling. The model is the data.
Unless you believe in the soul, then the human brain is just a very complicated learning architecture with a specific structure (which we freely know doesn't operate like existing systems...sort of, of course we also don't know that it's not just a convoluted biological path to emulating them for specific subsystems either).
But even your original argument is focused on just playing with words to remove meaning: calling something data doesn't meaningfully make your point, because mathematical symbols are just "data" as well.
Mathematics has no requirement to follow any laws you think it does - 1 + 1 can mean whatever we want, and its a topic of discussion as to why mathematics describes the physical world at all - which is to say, it's valid to say we designed mathematics to follow observed physics.
[1] https://www.neelnanda.io/mechanistic-interpretability/othell...
The existence of planets is "predictable" from the difference between the data and the theory -- if the theory is just a model of the data, it has no capacity to do this.
If you want to "do physics" by brute force optimization you'd need to have all possible measures, all possible data, and then a way of selecting relevant causal structures in that data -- and then able to try every possible model.
Of course, (1) this is trivially not computable (eqv. to computing the reals) -- (2) "all possible data with all possible measures" doesn't exist and (3) selecting relevant causal structure requires having a primitive theory not derived from this very processanimals solve this in reverse order: (3) is provided by the body's causal structure; (2) is obtained by using the body to experiment; and (1) we imagine simulated ways-the-world-might-be to reduce the search space down to a finite size.
ie., we DO NOT make theories out of data. We first make theories then use the data to select between them.
This is necessary, since a model of the data (ie., modern AI, ie., automated statistics, etc.) doesnt decide between an infinite number of theories of how the data came to be.