Unfortunately, Anaplan doesn't have a date/time concept (like Excel's NOW).
I've seen the following methods used to document a date/time stamp
One client manually exports the transaction history daily and an automated process picks up the file, cleanses it, and reloades timestamp information for selected types of transactions. This approach is not ideal, but does work well in certain circumstances... but breaks down with most, but not all, bulk changes (because bulk data changes often don't make the exact changes viewable when querying history).
Another client loads a date/time stamp to a single cell each time a particular process runs. They also document date/time for bulk loads (at the list item level). However, both of these are controlled by automated processes... getting this right manually is probably a non-starter.
I'd love to see what other folks have done... the community comes up with some interesting ways to get things done!
Yes, the user ID would need to be an Admin. Also, the history extraction can only be done manually (the processes after the extraction can be automated, but the extraction itself is a manual task at this point).