Is pressure lower than ambient on the pressure (bottom) side of an airfoil?
If the airfoil generates lift, pressure on the upper side has to be lower than on the bottom. Still, there can be suction (less pressure than ambient) on both sides.

For an extreme example, take the airfoil from US patent application 2004/0094659 A1 by Dan Somers. It tries to stabilize the boundary layer over the first 80% by creating an increasing suction over chord. The picture below is shamelessly copied from this application.



Ambient pressure is at a pressure coefficient c$_p$ of zero, and negative values denote suction, i.e. lower than ambient pressure.

All lift is generated by the highly cambered flap while the forward wing will only start to contribute lift once the angle of attack is increased from the current value of -2°. Note that airfoils for high subsonic speed show the same philosophy of a rooftop pressure distribution over their forward part with high rear loading. Such airfoils exhibit a high pitching moment and require a larger tail surface for stability, which blunts their advantage of low drag a bit. The plot below is taken from US patent 3,952,971 by Richard Whitcomb and shows just such a transsonic airfoil with a weak shock on its upper side.



This plot shows the speed difference ∆v compared to ambient, and again higher speeds which equal more suction are positive.

All those airfoils will develop a suction peak at the forward end of the upper surface and a corresponding pressure increase on the lower side once the angle of attack is increased. Now a Birnbaum-type pressure distribution will be added and at high angle of attack, this effect will dominate the pressure distribution and will ensure higher than ambient pressure on the lower side. This effect will be the more pronounced the thinner the airfoil is - a thick airfoil exhibits a stronger displacement effect which adds a little suction on both sides.


  hitting air molecules with the wings will cause them to accelerate


Not exactly hitting - it is air molecules flowing around the wing which will contribute a speed increase and hence a lower local pressure. This can best be seen by the pressure distribution around symmetrical airfoils at zero angle of attack. Note in the plot below that suction is on both sides and growing with airfoil thickness. Of course at that angle of attack those airfoils do not generate lift, but when an angle of attack is added, they will, and it will need a higher angle to push the bottom side of the thicker airfoil into the pressure region of negative c$_p$ values.



Inviscid pressure distribution of symmetrical NACA airfoils (picture source).


  Ambient pressure is higher than any wing pressure


Not quite: Note that all plots show a pressure peak at the nose and a pressure recovery to slight overpressure at the trailing edge. While most of the pressure around a thick airfoil at low angle of attack is indeed lower than ambient, the stagnation point will always ensure that this is not true for all of the airfoil.