In short, no . This is not possible in 99% of cases. Especially in a MySQL environment. NoSQL and other services such as MongoDB and other environments are different.
Run this script in phpMyAdmin for future use now (you already assumed that you were going to write a stamp).
ALTER TABLE Addresses ADD Column CreatedOrModified timestamp NOT NULL DEFAULT CURRENT_TIMESTAMP ON UPDATE CURRENT_TIMESTAMP;
You can also use NULL as well as DateTime Stamp for default values. You can also send PHP data to the MySQL field:
$stamp=$date=date("Ymd H:i:s");
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