When you open up FontBase for the first time you will see the Providers section in the Sidebar on the left, containing a single folder: "Google".
If you check your Root folder, you will see that there is no Google folder inside Providers. This is by design, it will appear as soon as you activate your first Google font. When you activate a font in this folder via FontBase, the font is downloaded from Google servers, activated and stored locally in your Root folder and can then be used as any other font file. Please keep in mind that this does require an active internet connection for the fonts that have not yet been downloaded.
If you'd like to remove the pre-loaded Google provider, simply right-click it in the Sidebar and choose "Delete". You can later re-add it by right-clicking the Providers section title and selecting "Import Google fonts".
NOTE: Google updates the fonts available via their proprietary API (used in FontBase) at a different rate compared to the list normally available via the Google Fonts page. If you see a specific font there that do not yet see in the app, downloading and adding it into FontBase is the best way to make sure you've got exactly the font version you're looking for.