The issuing certificate of the certification authority is, simply, a confirmation that the public key that you sent to the certification authority in the Cerfiticate request really belongs to you (otherwise everyone could pretend that he is the owner of the domain google.com or amazon.com). Since the certificate contains your public key, it cannot be prepared in advance. In addition, the response time depends on the type of certificate you requested. Simple certificates that confirm that the applicant (you) really own the domain take little time to generate. Usually CA sends you a link to an email from your domain, like firstname.lastname@example.org. You click on the link and confirm that you are the owner. Then CA generates a certificate and sends it to you.
But other types of certificates include much more verification, for example The certification authority should verify that your business really exists and is really properly registered, that your business resides at the particular address, etc. . This check can take many more days or even weeks. It takes a lot of effort, so the price is that much higher. But the certificate also confirms much more than other certificates.
In addition to domain certificates, there are other types of certificates, like S / MIME: to sign your emails, so the recipient can count that the email really came from you; it can also be used for email encryption. Verification and generation of these certificates takes even less time than for domain certificates. There are certificates for code signing, etc.
More details you can find on CA websites (I prefer not to promote any here).
To sign certificates:
The certification authority has a root certificate. It is the most important element of the certificate hierarchy. This is why it is stored with great security. For often practical use, this is not practical. This is why CA uses a root certificate (which is generally valid for 10 years or more) to issue certain signing certificates which have a shorter validity, such as 3 to 5 years. Shorter validity means less exposure and therefore less risk of compromise.
To the question: Yes, these signing certificates are created in advance.