I don't know that you can. The way a Chromecast configures is it broadcasts its own network that you connect a device with an account to. Once connected it does the configuration on Google's end, and allows you to connect that device to your home network for the purposes of streaming or casting. The thing is though, it doesn't have ports that would allow you to run custom firmware so you're stuck with a puck that you can't configure without a Google account as far as I'm aware. It relies entirely on you connecting to it as a host device to share data, updates,firmware etc.
Edit from Reddit: "You don't need a Google account but it's relatively complicated if you're not familiar with quite a few things. First you'll need to sideload another launcher like ATV. Then you need to disable the setup wizard and Google TV. All of this can be done with a simple app called App Manager which is an open source app you can get from GitHub. You'll need to go into settings then go to about phone and click build number seven times to enable developer options and then turn on USB debugging. The Chromecast is already set up to connect on Port 5555 depending on your IP address so after installing app manager it will detect that debugging is enabled and will connect to that port. You can disable any app very easily with it as well as many many other features that are very useful. As far as the Play store, you can also sideload the Aurora store which is the same as the Play store but you can login anonymously. Since the package installer doesn't work you'll need to install apps downloaded from Aurora with it. You can choose to do so in Aurora store settings. Also with app manager you can go into its settings and set the installer app as the Google Play store because some apps won't function unless they're installed or at least marked as installed from the Play store. "