You can prevent the thumbnails from being displayed when the gallery is loaded by setting:
showThumbsOnLoad="FALSE" - (for Large Screen Mode) - Thumbnail Options
showSmallThumbsOnLoad="FALSE" - (for Small Screen Mode) - Thumbnail Options

You can prevent the user from toggling the thumbnails on and off (by disabling the Thumbnail Button on the Button Bar) by setting:
showThumbsButton="FALSE" - (for Large Screen Mode) - Lite Options
showSmallThumbsButton="FALSE" - (for Small Screen Mode) - Thumbnail Options

Juicebox was not designed to default to fullscreen mode and requires a click from the user (on the Expand Button on the Button Bar) to go into fullscreen mode.
If you really want your gallery to go fullscreen as soon as the gallery is loaded, then you could try one of the following suggestions but please remember that Juicebox was not designed with this in mind so you might encounter some unexpected problems.

(1) If you link directly to a web page containing a gallery, then try adding #expanded to the end of the URL.
As an example, take a look at this embedded demo gallery: https://www.juicebox.net/demos/pro/embedded/
... and now go to the same URL but with #expanded at the end of it: https://www.juicebox.net/demos/pro/embedded/#expanded

(2) If you cannot use a URL to automatically expand your gallery, then you could perhaps use the Juicebox-Pro API method toggleExpand() (within the onInitComplete event) inside your gallery's embedding code to fire fullscreen mode when the gallery is ready.
Here is some sample code which you could use to achieve this.

<!--START JUICEBOX EMBED-->
<script src="jbcore/juicebox.js"></script>
<script>
    var jb = new juicebox({
        containerId: "juicebox-container",
        galleryWidth: "600",
        galleryHeight: "400",
        showExpandButton: "TRUE"
    });
    jb.onInitComplete = function() {
        jb.toggleExpand();
    };
</script>
<div id="juicebox-container"></div>
<!--END JUICEBOX EMBED-->

I hope this helps.

Edit:
Please note that if your gallery sets useFullscreenExpand="TRUE" (Lite Options) then neither of the suggestions above will trigger the Fullscreen API to go true fullscreen. (The gallery will expand only to fill the browser window, not the entire screen.)
This is due to a security feature of the Fullscreen API (please see here for further details) whereby the user must initiate the true fullscreen functionality via a click (on the Expand Gallery Button on the Button Bar).