Can a single-slit experiment demonstrate the particle nature of light?

I believe you have that backward. The two-slit experiment demonstrates the wave nature of light.

Light must be quantum because it interacts with single atoms and either has an effect or does not have an effect. It has to do that in a single place. It is established that this is because of the quantum nature of light and not the quantum nature of atoms.

But to create a two-slit interference pattern it must pass through both slits at once, so it has to be in two places. It must be a wave, and be everywhere.

Feynman resolved the paradox. Light is a particle and is in exactly one place at a time. But it has a probability function that travels like a wave, that decides the probability that the photon is in each place.

So a photon is a particle that appears in every possible way to travel exactly like a wave, except when it interacts with matter and acts like a particle.

There is no experiment that sends light through one slit or multiple slits where a particle pattern, (one line on the screen) is the result. The particle nature is only revealed when individual photons are sent through the slit or slits, but even in single photon experiments the wave nature is still present. Evidence of the particle nature is evident when individual impacts are recorded on the screen, yet they accumulate to create an interference pattern. The particle nature is never isolated in a slit experiment. The wave nature is alway present.

Actually it proves the wave theory. If the slit is narrow enough, then the light would diffract, which cannot be explained using particle nature, rather wave nature has to be used to explain diffraction, so it would actually prove the wave nature of light.