As Shopify is not a regular web host, they do not provide FTP access to the web space that they provide (which would be required to upload the gallery files) unless you have a Shopify enterprise plan.
This is noted in this Shopify forum thread.

Due to Shopify not providing FTP access to the web space that they provide, you would need to find an alternative host for your Juicebox gallery and then load the gallery into an iframe in your Shopify page following the Embedding in a Web Template Site instructions here.

There are many web hosts that offer free web space which would be suitable for hosting Juicebox galleries. Juicebox galleries do not require any special web server requirements (with the exception of Password Protection and the Download Button which require PHP 5.2.0 or later). Please see the System Requirements for details.
Try a web search with terms such as 'free web hosting' but please bear in mind that with a free hosting account, you may get little or no support, less reliability (more server down-time) and fewer features than with a paid support account.
A couple of free web hosts that I have personally used in the past and that you might like to take a look at are AwardSpace and x10hosting.
Please note that we are not affiliated with these web hosts at all. They are merely suggestions (and not recommendations).

If you do have a Shopify enterprise plan with FTP access, then you should be able to log into your Shopify web space, upload the complete Juicebox gallery folder via FTP (using a dedicated FTP program such as Filezilla) and then embed the gallery into your Shopify page using the baseUrl method of embedding documented here.
The baseUrl method of embedding is essentially the same the regular method of embedding but with a baseUrl entry in the embedding code pointing towards the gallery folder.

I hope my notes above help to clarify things and point you in the right direction.