There are two ways to restart Chromecast. Just follow these steps:

From the Google Home app
1. Make sure your mobile device or tablet is connected to the same Wi-Fi as your Chromecast device. 
2. Open the Google Home appUser-added image.
3. In the upper right corner of the home screen, tap Devices  User-added image to see your available Chromecast devices. 
4. In the top right corner of the device you'd like to reboot, tap the device card menu  User-added image Settings.
5. In the top right corner of the Device Settings page, tap the More button User-added image Reboot.

From the power source
1. Unplug the power cord from the Chromecast device.
2. Leave it unplugged for ~1 minute.
3. Plug the power cord back in.