To create a lift, the airflow speed on top of the wings should be higher than the airflow speed on the bottom of the wings.
That is correct. Lift is the result of a pressure difference between upper and lower side, and pressure is proportional to the inverse of speed squared if no energy is added.
But when you keep the engine on the bottom of the wings, wouldn't it hurt the lift as air flows faster on the bottom of the wings?
Note the point about adding energy in the paragraph above. As @JanHudec correctly points out, speed in the engine exhaust stream does not indicate suction. The pressure in the exhaust stream is still higher than on the upper side of the wing and lift is not diminished.
But friction drag is proportional to speed, so the higher speed on the upper side will cause more friction drag from the engine mount and nacelle. Placing the engine on the lower side puts it into a comparatively slow airstream. Also, the engine intake will slow down the air ahead of it (ram effect) and since the air that flows around the intake ends up on the lower side, this blocking effect of the engine intake causes less de- and acceleration of air, lowering losses. Adding the greatly increased volume stream of the hot exhaust gasses also keeps pressure up since all the volume behind the nacelle can be filled with exhaust gas. Adding the engine, therefore, slightly increases lift.
But the most important reason is maintenance and accessibility. The low-hanging engine is easy to reach and to inspect. That is a major reason why the "classic" layout that started with the Me-262 and was carried over to the passenger jets is still preferred. There have been designs with their engines mounted above the wing (for noise abatement), but that never caught on.
The next reason is cabin noise. By shielding the loud exhaust stream from the cabin by placing the wing between both, passenger comfort is significantly improved. This was especially important for the early jets with their high exhaust speeds.