For now, it looks like we can't stop it within JIRA Service Desk:
Cloud suggestion: Customize/Disable Welcome E-Mail to New Customers
Server suggestion: Customize/Disable Welcome E-Mail to New Customers
Please vote/comment on the suggestions, so the development team can understand your use case.
Maybe your email administrator can setup a rule on the email side, based on the standard contents of the "Welcome" email?
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