Hi there,
tricky one without custom development.
You could use a Header Element to display the full screen container with a background image:
https://docs.generatepress.com/article/header-element-overview/
Then to add the menu, you could try this plugin:
https://en-gb.wordpress.org/plugins/widget-shortcode/
Add the shortcode it provides in the Header Element Content.
You can then add a Navigation Menu Widget to that area.
That would provide the basics.