The shape of the wing is vital. It is curved on the top and flat on the bottom. This as you surmised means that the air on top of the wing has a longer distance to travel.
While we can’t see the air, we can see its effect. This is a video of an aerodynamic stall. That means the plane is going so slowly that the wing no longer provides lift.
Notice the strings start at the back of the wing. They start to wiggle first. The air is becoming decoupled. As the plane continues slowing the effect moves to the forward edge of the wing. This is the visible effect of what is happening.
The rule for this is to lower the nose of the aircraft. That allows the plane to pick up more speed and increase the airflow over the wing. The wing generates more lift, and the plane returns to flying instead of falling.
Sometimes Pilots screw this Flight School 101 technique up. An example is Air France Flight 447.
The plane was at 35,000 feet and entered a stall. It climbed at first and then stalled. It fell nearly eight miles to impact the water. The situation was easily corrected by simply lowering the nose. The aircraft would have picked up speed and stopped falling, allowing the pilots to regain controlled flight.
While it is not the only such example, it is one most of us heard about.