To expand slightly on Van der Waals:
As you probably know, electrons don’t really “orbit” around a nucleus. One can roughly approximate their behavior to instantaneously blipping in and out of existence in various locations around the positively charged center. We generally think of this as a probability distribution or electron cloud.
Now, at any one moment, all the electrons around a given nucleus are happy to stay within their defined orbital which we usually define as a shell within which we have a 90% chance of finding the given electron. However, those electrons might, due to sheer chance, momentarily ‘exist’ in an unequal distribution around the nucleus. Very briefly, electrons might pile up to one side of the nucleus. Being negatively charged, this inequality will - just for a moment - induce a dipole in the atom/molecule in question, giving it a positive side and a negative side.
This momentary dipole can induce other dipoles in the materials surrounding it, polarizing nearby molecules in the opposite direction. Opposites attract, and so simply due to the random motion of electrons, every molecule experiences an attractive force to other nearby molecules. This ‘dispersion’ force is usually swamped by other, more powerful effects like permanent dipoles or other electrostatic/polar interactions, but in some materials and at very close distances, the effects can be profound.
Additionally, by placing two very smooth plates together one can exclude air from the interface between them, resulting in what is essentially suction between the pieces.
To really see these interactions on a macroscopic scale, you need (as has been mentioned) two very smooth, very clean, very close surfaces. You can see a similar sort of effect with new microscope slides, although air pressure is playing the larger role here too.
I don’t know which forces are dominating in your case or what kind of glass you’re using, but your friend is, bluntly, wrong. Try looking at a piece of common glass under a microscope, if you have one available.