What you know is correct, and in fact a symmetrical airfoil produces no lift AT zero angle of attack. However, once you increase the angle of attack of the airfoil, the air over the top travels farther than the bottom, therefore travels faster, therefore has a lower pressure, therefore you have a net upward force on the airfoil- lift.

An airfoil with camber will produce some lift at zero angle of attack, and of course the lift increases from that point as AOA is increased. You would also find that such an airfoil will produce zero lift at a negative AOA, -2 deg. for example.