The cambridge website says "it’s the curvature that creates lift". NASA says the deflection of air creates lift. Therefore, a flat wooden board also produces lift at a positive angle of attack. The shape does have an influence on how much the air is deflected, but it is not the source of lift. The coefficient of lift from the lift formula is a combination of both the angle of attack and the effects of the geometry of the airfoil, which may have either a positive, negative, or no effect on the deflection.