But instead it shows the first image, and it's not even all of it.
What you are describing is the Splash Page.
The Splash Page is a placeholder for the gallery which is displayed by default on small screen devices when the gallery is embedded in a page alongside other content (like your web page's header) and may be too small to be usable.
The Splash Page is essentially an image link for the gallery which displays an image (by default, the first image in the gallery) and some text.
When the user clicks or taps the Splash Page, the gallery is expanded to fill the user's browser window (giving the images more space to be displayed).
For more information about the Splash Page and how Juicebox adapts to different devices and screen sizes, please see here.
If the gallery was on a page of its own (100% x 100% with no other content on the web page), then the Splash Page would not be used and the thumbnail page would be initially displayed.
If you had Juicebox-Pro, you could choose to not use the Splash Page by setting showSplashPage="NEVER" (in JuiceboxBuilder-Pro's 'Customize -> Splash Page' section). Using this setting, the thumbnail page would initially be displayed instead of the Splash Page on small screen devices.
Alternatively, you could force the gallery to be displayed in Large Screen Mode (which, by default, does not use the Splash Page) on all devices and in all browsers by setting screenMode="LARGE" ('Customize -> General').
If you chose to continue to use the Splash Page, you could customize it using the Splash Page configuration options.
By default, the Splash Page uses the first image in the gallery and the image is resized to fill (rather than fit within) the Splash Page and cropping may occur).
You can choose a different image to represent your gallery on the Splash Page (perhaps one that is more suited to a portrait style viewport and more tolerant towards cropping) using the splashImageUrl configuration option.
Unfortunately, all the options in bold above are supported by Juicebox-Pro only.
It is not possible to change the behavior of the gallery (with regard to Screen Modes and the Splash Page) using Juicebox-Lite (the free version).
I hope this helps to clarify things, though.