There are a couple of ways to handle this that I can think of.
- If you are tagging each row with the person that added it, then in the workflow/bot trigger, simply test count of rows for that person as part of the trigger criteria. If count is zero then trigger.
NOTE - when the automation executes the trigger, it happens on the server side and I think, in your use case of adding a row. it will still be zero at that time the trigger expression executes. If not, then test equal to 1. A bit of testing will confirm.
- If you are not tagging rows with the person adding it, then set a dedicated flag such as [Welcome Sent?]. If you have a Users table, this would be the perfect place to park such a column. Set this flag on the first row added to prevent additional additions from triggering the automation.