My registrar is Google Domains; there's no errors reported in the DNS settings or anywhere else. But Google's own DNS query at https://dns.google/query?name=xordle.xyz returns a status code 3 -- NXDOMAIN, or no such domain.
I tried transferring to a different registrar but it can't be transferred on account of it "not existing". I tried using Google Support; they weren't helpful in the slightest.
Do I have any options aside from just getting a new domain name if it doesn't resolve itself quickly?
Double check the Registrar Setup (top-right) in your domain zone that you are pointing to the right set of google names servers.
Name Server: NS-CLOUD-D1.GOOGLEDOMAINS.COM ... Domain Status: serverHold https://icann.org/epp#serverHold
"If you provided delegation information (name servers), this status may indicate an issue with your domain that needs resolution. If so, you should contact your registrar to request more information. If your domain does not have any issues, but you need it to resolve in the DNS, you must first contact your registrar in order to provide the necessary delegation information."