It begins when you realise all the physics examples are toy models, and reality is basically unmodellable. That physics is not mathematics, and the rules of inference in physics cases are the rules of reality -- not of mathematics. That what guarentees your modelling works is observation, that "hand waving" is something one does to force one's thinking to be empirical.

I suspect people who learn physics via the textbooks end up learning some paralllel reality which is closed-form and models engineered trinkets.

Physics isnt mathematics, and it isnt engineering. I think this is communicated in how its performed, in the emotional tensor of its practice. A good physicist has a healthy contempt of both.