Assumptions:-
a) You have GNOME or some other Graphical viewer enabled on VM e.g. Debian10 or Ubuntu version with Graphical View.
1- Enable serial port via Metadata.
** Process for the same is explained in this document - https://cloud.google.com/compute/docs/troubleshooting/troubleshooting-using-serial-console
Bottom line is - add a new key-value pair in Metadata
key - serial-port-enable, value- TRUE
2- Click open the VM's page and click "Connect via Serial Port". (may be, a stop/start be required).
** It might take some time to become alive. After connection is established, you will get access to the normal CLI.
** Provide your username and password and proceed as you normally would do.
3- go to https://remotedesktop.google.com/access and login via your google profile.
** More details are here in this document - https://cloud.google.com/architecture/chrome-desktop-remote-on-compute-engine
4- Select 3rd option - Set up via SSH.
5- In the "Set up another computer", click "Begin" and then "Next" and then "Authorise".
6- As per your GCP VM, choose/copy the command. This command, you need to run into your VM's CLI prompt as normal user.
7- It will ask to set a 6 digit pin and reconfirm it.
8- Now, open https://remotedesktop.google.com/access and select 1st option i.e. "Remote Access".
9- Click on it and provide your pin. ** you may save the pin.