Is my website even listed in Google?

Simply building a website, doesn't indicate that Google will index your website. It's easy to see if Google has listed your website by looking on Google for "site:mydomain.tld", e.g.: "site:YourDomain.com". If your query comes back with any listings in the slightest, Google knows you're there. If Google responds with the notorious "Your search did not match any documents", they've never heard of you - they just don't know that your website exists at all.