[superuser2]

All mainstream CAs issue certs through a fully automated process, and have for at least a decade. Generally you are required to receive emails sent to the administrative contact in WHOIS, put something in a DNS TXT record, place or file they give you at a URL they give you, or some combination of the above.

There are Extended Validation (EV) certs where a human verifies your ownership of a legal entity. Chrome presents these as a big green bar with the name of the corporation in the URL bar. Most certs (including Amazon's) are not EV certs.