Is it possible to start gnome-terminal always in fullscreen mode without menubar?

gnome-terminal --full-screen does what you want, although it is more keypresses than launching gnome-terminal and then pressing F11 to enter fullscreen mode.

You might, of course, create a wrapper binary called gt or whatever name you prefer:

#!/bin/sh
exec gnome-terminal --full-screen "$@"

Place it in your ~/bin directory and give it executable permissions.

1. Open the ~/.bash_aliases file with an editor of your choosing.
2. Add this line alias gnome-terminal='gnome-terminal --full-screen'
3. Either restart the terminal or type in source ~/.bash_aliases
4. Create a custom keyboard shortcut (via Ubuntu GUI, no need for fancy terminal commands) and set the shortcut to Ctrl+Alt+T.