We'll create fresh WordPress site with Dynamic Latest Post in Nav Menu installed. You have 20 minutes to test the plugin after that site we'll be deleted.
Add the link to dynamic latest post page, and the Archive page to Nav Menu.
Latest
The ‘Latest’ nav menu create the link to latest post page of Custom Post Type.
( orderby ‘menu_order’, ‘post_date’ )
When the new post is added, the link of ‘Latest’ is updated dynamically.
Archive
The ‘Archive’ nav menu create the link to the Archive page of Custom Post Type.
This Plugin published on GitHub.