The hard job of the experts is determining the minimal experiments to show people that will convince them of far reaching theories. For me that is the true measure of expertise in an educator.
Your good physics instructors will have you go through the photoelectric effect, the Millikin drop experiment, electron/beta ray diffraction experiments (possibly a few other). Maybe you build a transistor. You will see the necessity of quantum mechanics to explain your experience. Generally, at that point, you might question other quantum effects, but you are confident if you do the more complex experiements, you will see the necessity. You will probably have learned what those experiments are as well.
Black holes are another story. I recall still encountering astrophysicists that wouldn't be convinced of the necessity of their existence. Special relativity you can get to accept via the Michelson-Morley experiment or similar experiments proving the constancy of the speed of light. From there you can sort of accept a need for a relativistic theory of gravity. But the evidence for GR starts to come from complex astrophysical measurements that you cannot really replicate and need to trust the (processed) data. The gravitational wave signatures can be convincing if you already know the math... but too many people feel that a simpler theory is just around the corner--a simpler theory without the singularities. Dark matter and dark energy face similar (but with their own variations of) skepticism.