Acrobat Pro Navigation Pane Settings

Yes, the navigation pane can be controlled with JavaScript, although it is not documented, and not all setting are available. 

So to do this you need to experiment with the "doc.viewState" property to see what works.  

First, open a PDF and setup the navigation pane. 

Then run this code in the cosole window:

( you'll find a tutoial here on the console window - https://www.pdfscripting.com/public/Free_Videos.cfm#JSIntro)

this.veiwState.toSource(); 

If the pages panel is open you'll see something like this:

({ocgStates:null, overViewMode:2, overViewPos:240, overViewX:0, overViewY:0, pageViewLayoutMode:1, pageViewPageNum:0, pageViewX:-161, pageViewY:0, pageViewZoom:3.231109619140625, pageViewZoomType:1})

overViewMode and overViewPos indicate the navigation panel displayed and the width of the panel.   

Put this code in a document script to setup the viewState when the document is opened. 

this.viewState = {overViewMode:2, overViewPos:240};

All this and more is explained in this article (paid for content)

https://www.pdfscripting.com/members/Document-Navigation-using-View-States.cfm