There is a little catch-22 when you initially register a domain example.com : often the registrar will send emails to the person doing the registration and when you use [email protected] to sign up such messages can't be delivered, because that's a new domain that does not yet exist and has email been not set up yet.
So possibly you're more or less required to use an existing e-mail address from a different domain initially.
IMHO it depends a bit on what that initial address is if you should want to
later change the contact email addresses to an email address in the example.com domain.
If your organisation already operates their own domain example.org and you used [email protected] when registering example.com as secondary domain: I'd leave it be.
When you used a personal e-mail account from outside your organisation, i.e. a Hotmail or Gmail account: then I would change that to [email protected] or similar after your mail server/service has been set up. That domainadmin can then become an alias for a personal mailbox, that in the future can transition to their replacement, or a functional mail box for example.
Mandating the use of email addresses in your own domain(s) for all business communication, sign-ups and registrations allows you to get access to mailboxes from people that fall ill or leave the company and similar use-cases.
In your own domain domain you can re-enable mailboxes from leavers or configure mail forwarding when necessary as well i.e. when you find out that a provider will send a verification email to [email protected] when Bob already left years ago.
Often the email address is used for access recovery and access to the business mail address will also allow the company to recover access in relevant use-cases.
You might want to document that in your employee handbook or similar BTW. (There are obviously privacy implications.)
Related: https://serverfault.com/a/1062750/37681
