How can I build a page that generates random images from a gallery each time the page is refreshed?

Pardon my complete n00bness as I try to figure this out:

I run a daily cartoon/drawing website. I'm not a developer so I'm using the site builder called Pixpa which has worked well for my straightforward needs: daily update on homepage + archival galleries.

There is one thing I would like to implement that the site builder is not equipped for. I would like to have a page called "random cartoon" that, when visited, populates with a random cartoon from the archive.

I can create a basic page using the site builder and it has the option to add HTML to customize. Theoretically, I figure this means I could create this "random cartoon" page from scratch, but I don't know where to start.

One other note that may be an issue - the image files for the cartoon are not located in any one central folder/volume in the backend of the website. Pixpa does not have that function. So right now each cartoon exists on the site in a corresponding gallery and has been assigned a url such as "https://ift.tt/8pJ5d0c"

There are almost 700 cartoons so far, with more being added each and every day, so this is a major aspect of my issue...

In summation my question is - how and where should I organize my images so that I can implement this "random cartoon" page most efficiently, and once I have completed that organization, what CSS should I use to create the functional page?

Appreciate any insights you may have. Thank you in advance!