suggestions are welcome
Don't schedule the task in your script. Instead have it create a file that contains the email address of the user and any other user specific data. Save this file in a folder maybe named something like C:\WelcomeQueue. Format the filename using a timestamp, like 2021-05-04-10-37.msg.
Manually create a scheduled task that executes every hour or every half hour. Have this task execute a SendWelcomeMail.ps1 script.
When the script runs it does a Get-Date and subtracts 60 minutes to build a variable that can be compared to the file names in C:\WelcomeQueue. Actually, you could compare against the file name or the date created attribute. The intent is to identify files that were created more than 1 hour before the current time.
Read those files one by one, send the welcome email, and then delete the .msg file. If there are no files found, the script just terminates.
Be sure to add some logging functionality into SendWelcomeMail.ps1 so that you know what it's doing.