In this system, SFTP will be used to upload large video files to a specific directory on the server. I am writing a PHP script that will be used to copy completely uploaded file
As @jcolebrand stated - if you have no control over upload process - there is actually not much you can do except guessing (size/date of file). I would look for a server software that allows you to execute hooks/scripts before/after some server action (here: file transfer complete). I am not sure though whether such software exists. As a last resort you could adapt some opensource SFTP server for your requirements by adding such a hook for yourself.