Unlike other posts in the community, the date does not display as a hover-over tooltip. It summarizes the date as “1 month ago” or “6 months ago” or “1 year ago” but it’s not possible to get the exact date.
This might be more a bug, but it’s a fix that’s needed eventually to bring messages to parity with other posts (not to mention expected functionality when compared to the proliferation of direct messaging on other platforms in our day-to-day).
Admins and community managers will have backend options to get this data for their own personal private messages, but end-users are more likely to be visiting a community less frequently and viewing an older message that they can’t find the date for (if it’s >30 days old).