We have the Git client available, so you can SSH in and pull your own Git repo from Github, Gitlab, Bitbucket or wherever, but we don’t yet have the feature released where you can just “git push kinsta/my_site” and it gets deployed automatically. This part is coming soon.
Right from launch you can create a deployment script in a few minutes that will SSH into your Google Cloud Linux container and pull once you’ve pushed a new version to your remote. So instead of doing “git push kinsta/my_site” and be done with it, you’ll have to add “git push kinsta/my_site && ssh email@example.com && cd /www/my_site/public && git pull”.
Many of our customers are using WP Pusher as well for this.
If you have questions, our support department will be happy to help once you are up and running.