Suppose I own the domain example.com and I want to send emails from addresses like firstname.lastname@example.org. However, I don't have any actual mail account or mailbox set up at this domain (nor do I want to).
I've configured a catch-all redirect, so any message to email@example.com is being forwarded to an external address - say, a gmail or hotmail address.
So I do receive email sent to firstname.lastname@example.org (on the external address), and now I would like to be able to send email from addresses like email@example.com or firstname.lastname@example.org.
What would be the general approach for this? I guess it also depends on what kind of email client I'm using to send email, such as Thunderbird or Yahoo or Gmail or Outlook. But how or what do I have to configure in my example.com's domain and email settings (if any) to make this work?
My problem is that everything always seems to assume that an incoming and an outgoing address come together and are associated with an actual mailbox or email account.
Important: I want to avoid my outgoing mail being marked as spam. So I don't just want to spoof my domain name or something fishy like that. I own and control this domain and want to set this up correctly.
P.S. My domain is registered and hosted at a hosting provider which comes with an SMTP server.