I don’t think you can. On the other hand, if you register a Google account, use a secondary user on your phone to login, install the app and activate the Chromecast, I think you can subsequently use it without the Google account. Delete the secondary user once you’re done with the setup. You wouldn’t have given Google any useful data and you’d have cost them some.
Well I don’t know what OP is planning to use it as, but desktop VLC can cast to Chromecast on the LAN for example.