...not by the time when they were made but by the time they were transmitted on to the server.
A little elaboration on the nature of your server may perhaps spark some ideas.
- Does the server side file system provide local file creation/change/access time?
- If server is a FTP server, can it provide new file notifications or can it trigger a notification script of some sort?
- Are there packet capture or transmission logs that may contain the filename, or can it be set up?
In short, look for anything that can help provide a list of <filename>,<server_time> records for further processing.