I think the requisite elements were in some way known well known, at least identified, decades before the Wrights, before 1903: Lift, propulsion, some form of stability and control. The problem was less in identifying these, and more finding practical solutions. The mechanically-experienced Wrights applied their knowledge of lightweight bicycle structures to solve the problems.
But they did more: They saw the deficiencies in their competitors' designs, and studied and experimented to overcome those problems. Experimentation yielded efficient airfoil designs, not only of wings, but of propellers as well.
And so by the time they had settled on a physical design of the Flyer, the challenge was to fly it. They had prepared for this by flying a series of gliders. Here they learned the need for three-axis control.
So the Wrights contribution was not so much a single invention, but in perfecting the combination of known arts to create a working vehicle.