I have done something similar but with a couple of variations.
As my site has a vertically scrolling home page, I want to encourage my visitors to scroll through the sections on the home page to view the main "foot-stompers" before going anywhere else. What I did was create several timelines:
One makes a burger menu fade in. This is triggered by an action in the main timeline that is set at 8 seconds. It gives the visitor enough time to discover the vertically arranged sections instead of automatically going for the menu. (Each section has a "learn more" button for cycling through one or more pages and back to the same location on the home page.) When the visitor reaches the bottom of the page and they hit a button to scroll to the top, the menu is there waiting for them.
There is another timeline that extends / retracts the menu along with an invisible object. When the menu is extended the invisible object pops over the burger and retracts menu when clicked (a down-and-dirty toggle).
Then, rrather than using a menu item for simply jumping to a page, I have designed things so that the menu retracts before the jump.
To do this I created a simple timeline for each individual menu item. Each one has a timeline action that, after allowing time for the menu to retract, triggers the jump to the URL for than menu item.
When clicking on the menu item, this triggers the menu retraction, plus it plays the timeline for that menu item, which triggers the jump to the associated URL.
For a site created in Hype (which mine is) you may wish to speed up initial loading by splitting the site into multiple Hype docs. If the site were not media heavy I would use a similar approach for jumping between scenes.