My question is, after this point, can Alice reclaim her domain? Is there any way to automate verification of domain name ownership outside without DNS?
She hasn't lost the domain, she's lost the ability to control its DNS at the provider she's currently using (the nameservers she set).
So as sibling says it's a case of changing the ns to some other provider, or else I suppose a support case to somehow prove you do own the domain, so please assign control back to your account.
Well, if the email address you use at the registrar is under the domain the attacker now controls, they can hijack it and potentially escalate to taking over your registrar account as well. Hopefully you have 2FA set up and your registrar enforces it properly.
Thinking back more I realize that when I first registered my domain there was no money involved. I remember when ethical discussions of charging for domain names. The justification is that buying the domain name proved ownership. I suppose it was also meant to discourage people piping dict into the registration process. There was a land rush for nouns such as pets.com.
