For Exchange on-premises created mailbox, you could use the Script Agent to send emails to newly created mailboxes by following the article: Send Welcome Email to New Mailbox / New Users.
For Exchange online, there doesn't exist Scripting Agent. There doesn't exist Microsoft blog introduce about it. But, you could use the script that contained in the article AndyDavid provided. That script is used to check mailboxes created within 7 days, then send a welcome email to that mailbox. You could add it to a scheduled task to run weekly.
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