What is there to prove? You can register your own domain (avoid exotic TLDs), wait a few months to build trust, and use an email setup script like Luke Smith's to set up Postfix/Dovecot.
Before you start sending email, use mail-tester.com to check that DKIM is correctly set up and that your IP is not blacklisted.
Before you start sending email, use mail-tester.com to check that DKIM is correctly set up and that your IP is not blacklisted.