If you want to add the date on the property unit/card in front end (will apply to all property units – including shortcodes)

Details are stored after 3.1 theme update in:

<?php $my_date =get_the_date(); echo $my_date; ?>

If you want to add the date on property_unit/card in user dashboard

edit dashboard_listing_unit.php and add the same code as above

<?php $my_date =get_the_date(); echo $my_date; ?>

If you want to change the date format please look over the official documentation

https://codex.wordpress.org/Function_Reference/get… and here