I.e. air cannot "pull" anything anywhere.
So the depression above the wing is indeed "pulling up" the wing more than the surpression below the wing is pushing up the wing.
So no, the top of the wing is not pulling the wing upwards. The air beneath is "blowing" the wing upwards.
Also terms like "push" and "pull" really confuse the mechanics here. What matters is that a net upward force is being generated, with positive pressure acting on all sides of the airfoil. There is more pressure acting upon the lower surfaces than on the upper surfaces, but at every point the pressure is positive because it is surrounded by fluid (not in a vacuum). If you integrated the pressure acting on a lifting airfoil and computed the average direction, it would be pointed up.