Can I add an additional outlet using an existing outlet that has no ground wire?
There are ground wires there, they're just buried in the back

In your photos, I can see some bare copper wires in the back of the box. These are the ground wires you are looking for, and you'll need to get them pulled out as far as they can go, then nut them to a box grounding pigtail screwed to the box and to another pigtail that goes off to the receptacle.