Set up a field that just has the TODAY() function as your formula. Then in the “update record” part of the automation you can use that as the dynamic data for your field. It won’t be time stamped aside from the date but it sounds like that would acco...
+1 for this option - it looks very sloppy to have an empty column always be the first one, particularly in interfaces where it's supposed to be a more "presentable" alternative for nontechnical users.