No such plugin for moodle.
Would have to be done on Google end anyway.
See:
https://support.google.com/sites/answer/6372880
Work Around ... Google Sites
Create a single page google site that has only a link to your moodle.
If site is restricted to your domain users they have to login to
google to find the sites link and then click the only link in the page ...
that of your moodle.
Since they are already logged on to Google, Moodle should detect user
is already authenticated in Google and should not have to login again.
The following is open to all but yours could be restricted to your domain users.
https://sites.google.com/sosoftexas.org/37sosmoodle/home
Yes, it requires some clicks ... but ... free work-around.
Dunno how much it would cost to hire a Google Developer to build such an app.
'SoS', Ken