The Google search feature is not offered as an option in the version of Firefox that comes installed in Linux Mint. You can add it with the Manage Search Engines feature, but when you do, you will notice that there are no search suggestions when you start typing a search term.
To add Google search suggestions, you need to edit the file
google.xml, located in the searchplugins directory, inside your
Firefox user profile. In my case, the full path for this file is:
/home/marios/.mozilla/firefox/mwad0hks.default/searchplugins/google.xml
Yours should be similar, and the command locate google.xml can help
you find the path.
Edit that file, and add the following line:
<Url type="application/x-suggestions+json" method="GET" template="https://www.google.com/complete/search?client=firefox&q={searchTerms}"/>
...somewhere before the closing </SearchPlugin> tag. Restart your
Firefox, and suggestions should now work.