First you would need to get OAuth 2.0 working.
After that it's just calling the correct URL from the Google Contacts API to edit contacts.
All I need is a small example that adds a contact, then from there I develop what I need.
There is no "small" example.
Getting OAuth 2.0 to work is a challenge all on it's own.
In FPC there are libraries in fpc\packages\googleapi\src but I haven't tried those.
I'm also not aware of any examples which use those libraries.
For Google Drive/Calendar/OAuth 2.0 I once created a "simple" example:
https://github.com/rvk01/google-oauth2Using it to add "Contacts" should be relatively easy.