surround it by nohup and put & at the end of the command.

it would be better to run the command using the key combo of alt + f2 and then putting the command there instead of using a terminal window so that you don’t have to bother with nohup.

If you use kde, you can search for “profile manager”, and it will show up, and can be launched from the app menu.

At least works for me. Before this was added, the KDE search/app menu also lets you run commands directly, so I would just run firefox -p in there. No need for a terminal.

Instead of disowning use exec or xdg-open

If you don’t want to fiddle with a terminal at all you can just make a keybind/shortcut. Depends on your DE or WM as to how to do that.

Why did the other commenters parse the title as a question? I expected directions from OP.

In the terminal session you launched firefox from:

Ctrl-Z  # Temporarily suspend process
bg      # Put that process into the background
exit    # Cleanly close the terminal session

Or launch Firefox (or whatever application) with a ’&’ at the end to put it in the background from the start.