Here's something weird about this date stamp business: I use Carbonite, and when I download a photo from my cloud file onto a different computer, it has the date stamp of the day I download it, not of the day I created it. Don't know what that would mean for the OP, however.
My understanding is the server would have the stamp of the original upload if that file, though I suppose a new version could change that. Your download will have the download date, because that's the date the downloaded file will be "created" on your computer, though the file may very well have other metadata relating to the creation date.
There is no requirement to do a search, and lots of people don't. It's a good idea to have one done, however.
What Steerpike said. Of course, that depends on a lawyer knowing that. If they're bringing in computer forensics, then the computer expert should know this. Although, there are times when the court-appointed experts turn out to be bogus. I've seen that before. Anyway. I wouldn't put any money on that, either. Hard to do, but I doubt that's good enough for a court. I've only seen a server log that records access and creation information. They're all different, though, so I dunno. All such a log would do is show that x file was uploaded or accessed or modified at x time. So unless their log is not accessible to the user AND is secure AND it contains all of the exact information that was edited or modified, etc., then I don't see how that would help.
Apparently there is such a thing as a timestamp authority. I have no idea how courts feel about them. But that would only work if you see the issue coming.
Eh, that's going to cost some money. DigiStamp, for example, will run about $10 a month. For what GazzaJohn wants, an online copyright registration is much cheaper.