Yes. Create a batch program with the needed switches.

See -new-window <url> and -new-tab <url> ooptions below

Here is an example (on one line only);

C:\PROGRA~1\MOZILL~1\firefox.exe -no-remote -P Firefox_v_57

https://developer.mozilla.org/en-US/docs/Mozilla/Command_Line_Options

Usage: C:\PROGRA~1\MOZILL~1\firefox.exe [ options ... ] [URL]
      where options include:
 
 -h or -help        Print this message.
 -v or -version     Print Firefox version.
 -P <profile>       Start with <profile>.
 -migration         Start with migration wizard.
 -ProfileManager    Start with ProfileManager.
 -no-remote         Do not accept or send remote commands; implies -new-instance.
 -new-instance      Open new instance, not a new window in running instance.
 -UILocale <locale> Start with <locale> resources as UI Locale.
 -safe-mode         Disables extensions and themes for this session.
 -console           Start Firefox with a debugging console.
 -jsconsole         Open the Error console.
 -browser           Open a browser window.
 -new-window  <url> Open <url> in a new window.
 -new-tab     <url> Open <url> in a new tab.
 -preferences       Open Options dialog.
 -search     <term> Search <term> with your default search engine.
 -setDefaultBrowser Set this app as the default browser.

@FredMcD and others...

Thanks for your reply.

Could you please tell me how to create a actual shortcut that I can click on, bring me into private mode and on to Google? I'm a bit perplexed and lazy.

I could then use your model to learn from.

Cheers! :)

Create a new Text file. Give it a name like; Clouds=Private.txt (example) Write the command in that file using the command switches in my last post. If you need help, tell us the site name and its link.

Rename the file by changing .txt to .bat making it a batch file. Try the batch file. All done.

@FredMcD -

Here's the solution, using the commands from your link given above:

https://developer.mozilla.org/en-US/docs/Mozilla/Command_Line_Options

In the Target area of the shortcut...

"C:\Program Files\Mozilla Firefox\firefox.exe" -private-window google.com

That's it!

Thanks. :)