I hope your having a wonderful day.
From my understanding, you can use this documentation you access the GUI version of a Debian instance [1]. Additionally, these two documentations [2] [3], should be able to explain to you why your experiencing an error when trying to use the GUI version of Debian on Firefox.
Furthermore, if the solution doesn't work, you could try following these instructions which could potentially fix your issue [4]:
1: Login to your server via this command: "ssh -X root@yourIP"
2: Edit /etc/ssh/sshd_config file and add this line to it: "X11UseLocalHost no"
3: Restart sshd for Debian with this command: "/etc/init.d/sshd restart"
4: Check your DISPLAY by running this command: "echo $DISPLAY", once done you should see this "yourIP:10.0
5: Now it should work so check to confirm
Best Regards,
Kevin
Google Cloud Platform Support, Montreal
[1] Debian GUI:
[2] Firefox GUI:
[3] Error:
[4] Possible Solution: