Issue #2676 might serve as an starting point on how to implement this.

Should we implement the "navpanes" parameter?
In Adobe Reader the "navpanes" are separate from the toolbar, but in pdf.js these can't be acessed if the toolbar isn't visible. I suppose that you could just hide the sidebar button if "navpanes=0", but do we want to do that?

#9414 was closed with a reference to this issue, but I'm not sure if the parameters are the same as "auto-hide" toolbar. In case someone is searching for a workaround to gain space or some different ideas of implementation, create a userContent.css in profile>chrome with the following content (instead of hiding the toolbar completely, it's just made transparent:

/* https://support.mozilla.org/de/questions/1119523 */
#outerContainer #mainContainer div.toolbar {
/display: none !important; / hide PDF viewer toolbar /
opacity: 0.5 !important;
}
#outerContainer #mainContainer #viewerContainer {
top: 0 !important; / move doc up into empty bar space */
}

I opened this: https://bugzilla.mozilla.org/show_bug.cgi?id=1807490

And was directed here - what's the status of the various unimplemented pdf parameters in pdf.js?