If your device is still connected to an existing Wi-Fi network, you can follow these steps to change the Wi-Fi network it is connected to. See the "If your speaker or display is currently connected to a Wi-Fi network" section.
If you've already changed to a different Wi-Fi network, try these steps:
Instead of factory resetting your speaker or display, if you're comfortable changing your router settings, you can change your new Wi-Fi network name and password in your router's settings to be the same as the previous ones. Your device should then automatically connect to the Wi-Fi.
Have a look at the Google Nest help center link below for more information about changing WiFi networks on Google Home or Google Nest speakers and displays.
Thanks for the help davidking and Cathal_S!
McFab, checking back if the shared links and suggested steps above help. Feel free to respond to this thread if you have additional questions or concerns and I'd be glad to answer it for you.
Just checking in to make sure that you our my response. I'll be locking this thread if we won't hear back from you again in 24 hours. Should that happen, feel free to create a new one if you have more questions or have other concerns in the future.