Integration with Google's calendars just works though, has done so for years — use the Lightning add-on and the Provider for Google Calendar add-on.
There's lots of outstanding bugs unfortunately.
See https://bugzilla.mozilla.org/show_bug.cgi?id=1314185 - earliest dependent bug is 8 years old.
Both of those add-ons have always been clunky and brittle for me. They have caused me to miss appointments and have also occasionally messed up my contact data.
I would never, ever use these add-ons for work.
See viraptor's comment for links to reported bugs: https://news.ycombinator.com/item?id=16340039