I have a domain on GoDaddy, and a website hosted on Google Cloud. I have pointed the nameservers to google, and my website works if I go to www.mysite.com but not if I just go to mysite.com. I did the forwarding option through godaddy, so it should redirect, but now the support there is telling me it needs to be done on the Google side since the nameservers are there.
From my SO research so far, I understand it can't be adding records to my DNS (though I'm not sure why), and it can't be done through my bucket. I find it hard to believe this is impossible - is that true? Is there something I can add on my DNS records?
Here's what my records look like on Google Cloud DNS.

All the google resources point to GoogleDomains tutorials, but since my domain is on GoDaddy they aren't useful to me.
You could just create two DNS zones,of public type, one containing www. domain .com. and the other without www.* ,just the domain.com.
Why do you need a single zone for each domain? Because the property name "dnsName" in the API version is a single value. So having multiple DNZ Zones, one for each domain for subdomain could solve your issue.
Or you could just "export a domain" (after being unlocked by third party domain provider) to Google Domains:
From Google Cloud Console go to:
Afterwards you could proceed to configure a DNS for the domain. You will have 3 options to configure the DNS for the domain: