At the outset I would like to say that I think this is an important question if only because it highlights a misunderstanding about Date Added. And this misunderstanding has not, to my knowledge, been addresses adequately in Ask Different.
Further, I am making this answer to explain why I don't consider Date Added to be metadata belonging to a file. And that is is spite of mdls
and Finder presenting it as file metadata.
Consider a file which exists in two folders using a hardlink. The date added is then different for each apparent instance of the file.
Hence the Date Added metadata can't belong just to a file. It pertains to a conjunction of file and folder.
To put it another way, create a hard linked second instance of a file in a different folder. The two instances of the file will correctly have different Date Added values even though they are the same file on the disk.
So Date Added of a file is meaningless without including the folder.
Just to add to the above, here is a sequence that would lead to a nonsensical situation. Consider: 1) a file added to your Downloads folder 2 weeks ago; 2) create a new folder (creation date would be today); 3) move the file from the old to new folder preserving (if you could) the old date added. Now you have a file which was added to the new folder 2 weeks before the folder was created!!
Putting it very firmly, Date Added only has meaning as the date when a file was added to its present folder. Make a hardlink, move a file or folder, or duplicate a folder and the Date Added (of file to folder) must be different.
Any hack to avoid this is always going to be hack. The only known hack that I have found involves modifying the system date and whilst that is ingenious, I really don't think it is to be recommended.