Create a new, blank project first. After unzipping the file contents on your own machine, you can then drag-and-drop all the files into the file uploader, which supports multiple file uploads. However, the uploader doesn't currently support folder uploads—you'll have to create the subfolders first, and then upload the files into them.
Alternatively, you can upload your files via the git bridge (which does support folders). After creating a blank project, git clone it to your machine. Next, copy your files from the .zip into the project folder on your machine, and then git commit and push. These links may help to give more details: here
and here.