Creation dates

You could do a Save As on both files--if it happens fast enough, they will have the same info (although the seconds may be different).

Do you by any chance want the modification date rather than the creation date? The only reason I could think of wanting the creating date would be if someone was checking up on when I created a file--but usually it is the modification date that really needs to be checked.

You could use a text variable in InDesign with the date you prefer. The variable could contain the creation date, the modification date, or any custom date you want.

Setting the creation fate of the PDF to anything different to what it is would be misusing the metadata. It has a specific meaning: when the PDF itself was created (the file made, not designed or approved). It isn’t for arbitrary setting of dates to match a project or similar. 

You cannot hide the PDF file's creation date.

           - Dov

The PDF file creation and modification dates are not “informational” fields that can be arbitrarily set. Thus you cannot synchronize the InDesign file's creation time stamp with that of a PDF file created from same.

            - Dov