Although Google sites may not support FTP access and you certainly cannot upload files or folders to your Google site in the traditional way, you can have the appearance of having added files and folders.
To add a folder, click on Sitemap, then the "new page" button:
Then we give a Name, use File Cabinet at the template type, and then we can put it at any level (in the following picture, I am putting it at the top level).
To add a file under this Downloads folder, we click "Add file" while in the "Downloads" page:
The steps after this are easy.
Let's say we wanted to add a folder under Downloads, called "WebDownloads"? This is easy, we set the location to be "Downloads" when we create the page:
Although this is not perfect, you can still use it to organise files into folders.