Hi Bmcenany,
We don't know when, or even if, the internet search box will return to the Cox home page.
It sounds like creating a shortcut to www.google.com might benefit you. You can create a shortcut icon on your desktop or add a shortcut on the button bar of your preferred internet browser.
For articles on how to create a desktop shortcut, go to http://bit.ly/2kn2Oef. For articles on how to add a favorite to the button bar of your browser, go to http://bit.ly/2xRxozm. I hope this helps!