In WordPress There are 2 dates, the publish date(when the property is added) and the edit date(admin – edit property – edit date).
The shortcode/property list always uses publish date. To force the property to appear as if new again it will mean to publish it again and that is not a solution.
If you wish for the properties to be sorted by Edit date, it is pretty complicated as this requires massive code changes.
We cannot make the code for you, unless you wish custom work.
Also, with custom work, we are not 100% sure that this will work properly as this is a complicated and very risky change.