I don't know, is "we've never seen this page on your site before" a valid defense against a DMCA claim? If I understand DMCA correctly, ignoring the claim means risking a lawsuit if you're wrong about the content not being owned by the claimant.
So it's my content, on a domain I no longer own or control.
How could I prove to Google that the content is mine?
You take over expiring legitimate domains, and ideally immediately (before Google notices) put up almost the same content, but with a link to whatever site you're actually interested in giving better search ranking to.
Repeat this 1000x and you can apparently make enough headway that people put time and money into the approach.