I wonder how much Google Nest charges the battery on the doorbell before they're sold. When installing, did you plug in the doorbell using the supplied USB cable, as shown starting at about 1:27 in the video on the page below? Is that where nothing happened?
If the doorbell is plugged in with the USB cable and the status light is flashing white, it should be charging, and it should be solid white if fully charged.
If you're getting nothing at all, perhaps you need to contact Support (https://support.google.com/googlenest/gethelp) to see if you have a faulty doorbell.
Since this thread hasn't had activity in a while, we're going to close it to keep content fresh. Feel free to submit another post, and provide as many details as possible so that others can lend a hand.
As we got our resolution here, I'm going to mark this thread as resolved. I'll be locking this thread if we won't hear back from you again in 24 hrs. Should that happen, feel free to create a new one if you have more questions or have other concerns in the future.
Thanks for chiming in, Archie.