There are several contributing factors which will affect the speed at which your web page will load.
(1) The speed of the web server hosting the site.
(2) The speed of your own internet connection.
(3) The number of external files (JavaScript and CSS) that your web page loads.
(4) The file size of the gallery images.
(5) The value of the imagePreloading configuration option.

You have little or no control over #1 and #2 but you can certainly check the others.

#3 Check that your web page loads only external resource files that are required. If there are any redundant files (for example JavaScript libraries which are not actually used on the page), then remove them and this should help with the initial load speed.

#4 Make sure your image file sizes are not too large. When creating a gallery with JuiceboxBuilder-Pro using the default settings (of 1024px x 768px at 80% quality), the resulting images will likely be approximately 120KB each.
This is usually a good compromise between file size and image quality for web gallery use.
If your images are substantially larger than this, then you might like to try reducing the file size to see if this helps.

#5 Try changing the imagePreloading configuration option (in JuiceboxBuilder-Pro's 'Customize -> Main Image' section) from the default value of 'PAGE' to 'NEXT' so that when the gallery is initially loaded, only the next image in the gallery is downloaded and cached by the browser (rather than all the images on the current thumbnail page).

Hopefully these suggestions will help.