Thanks for visiting the Community — let me help you out.
A few questions: are you using a public or private network? If you're using an iOS, could you try going to your phone's Wi-Fi settings? Then, connect to the Wi-Fi network that matches your Chromecast device. Look for something like ChromecastXXXX. Go back to the Google Home app and proceed with the setup. If the issue persists, try resetting your Chromecast and reinstall your Google Home app.
Let us know how it goes.