You can go into the web map's JSON, using something like the AGO Assistant, and edit the popup settings, as detailed in this solution:
EDIT: I replied too quickly, that won't help you in an AGOL web map. That setting isn't in the web map's JSON, but the viewer app itself, which you won't have access to in AGOL.
The dock popup in Map Viewer is stored on a browser cache basis and is not stored in the web map at this time.
@RussRoberts Is it possible to change the popup location of a map using another app let's an Instant App template?
You can adjust the docking placement in instant apps under the Step 2. About section.
Cheers Russ, this helps 🙂
Thank you both. I have created a web app instead of a web map. Is there a way to have the pop-up open docked by default?