Hey @iMorpheus, welcome to our Community.
I'm afraid that there's no way to archive a file in Dropbox; you can only delete it, if you don't it to show up in your account.
I would suggest taking a look at Emma's tips here and then post your idea on our Idea board, for other users to up-vote.
That way, if your idea gets attention, our team can consider it for future updates.
Let me know if you have any questions!