If you can't see the File Manager in cPanel, make sure there are no "collapsed" sections of the control panel. See the attachment below so that you can see where to look. If you know how to use FTP which is easy to use, you can use that to upload your files. I suggest using FTP if you're uploading large amounts of files, especially small files.
For FTP, the site address is
ftp://yoursiteaddressgoeshere and your username and password is your cPanel user and pass. Upload all files to the public_html folder.