I think without understanding Bernoulli's principle, wing design, etc. one could still manage to "discover" flight by experimentation. E.g. holding your hand out when traveling at speed you feel the effects of lift change as you change the angle of attack wind => your hand.
The Wright brothers were clever fellows. Rather than starting with building a powered aircraft right away, they creeped up to the problem by building gliders first. When they were disappointed with their first gilders they built their own wind tunnel to test different wing designs. After many tests and iterations they finally advanced to the Wright Flyer which flew under power in 1903.
The Wright Brothers were systemic in their design of aircraft. They kept detailed notes of their experiments for later use and improvement. Just bicycle mechanics they were not.
The Wright Brothers studied the physics of flight extensively, and it can be argue that they understood it better than anyone alive at the time, leading to their eventual success. In fact, they received 16 nominations for the 1909 Nobel Prize in Physics. Here is an article exploring why they did not receive it.
It depends a bit on what you call 'physics of flight'. The Wright brothers were very clever, systematic experimentators, as Asmalfly pointed out. They understood that an engined aircraft is just a glider with a propellor and an engine, so they concentrated on glider design first. They also solved the question of controlling the plane with gliders. Many constructors didn't think of the question of how to steer the airplane, once it is in the air. This often led to short flights ending in a very hard landing. They understood that a propellor is just a wing that rotates. They also managed managed to design their own engine, which was better than anything they could buy.
As for the physical question, why wings generate lift, the Wright brothers didn't contribute to this question to the best of my knowledge. The flow pattern of the air along the wing possesses a property that is called 'circulation'. The lift (force that stands in 90 degrees to the air flow) is caused by the circulation. The mathematical theory of circulation and lift was developed by Martin Kutta and Nikolaj Zhukowski.
Martin Kutta formulated a principle called Kutta condition, which states that the flow around a wing has exactly the amount of circulation that is needed to make the part of the flow that goes over the wing and the part of the flow that goes belong the wing meet at the same speed at the end of the wing. In order for this to happen, the end of the wing has to be sharp.
The question why the flow around a wing assumes exactly this amount of circulation was solved by Ludwig Prandtl. He showed that little turbulences in the boundary layer (a small layer of air around the wing that stays glued to the wing due to friction) controls the circulation around the wing. Any flow pattern around the wing that does not fulfill the Kutta condition is corrected by little turbulences that fall out of the boundary layer.
So I would say that the main people who solved the question of physically understanding subsonic flight are Martin Kutta, Nikolaj Zhukowski and Ludwig Prandtl. The Wright brothers were very smart, systematic experimentors, and they had a few good insights, but I wouldn't say they physically understood flight.