Can a small camera possibly have a large lens in the front?
There are really "large" lenses. This search is not the biggest one, but the look of it is great.
But you are referring to a large diameter compared to the depth of it.
Yes, there is a limit. The image on the left is a diagram of an f1 lens, where the green diameter and the red focal length is the same.
The second image has the focal length reduced by half, so it would be an f0.5 lens. There is a point where the light simply does not bend due to refraction anymore, so yes it has a limit.
That limit depends on the material used. I assume there could be several hacks to overcome this, for example using an insect-like array of lenses, similar to radiotelescopes arrays.
The limitation is givven by the Index of Refraction. For more information you can explore this: https://en.wikipedia.org/wiki/Refractive_index
Regarding the image, it is not that extreme. The image is not exactly isometric but it looks close so here are some lines "measuring the example"
So that example looks like a lens close to f1