In order to fully function, Wyze cams have to connect to WyzeHQ servers (over the internet) when they power up. Even if the camera had been previously configured for continuous recording to the SDcard, they still require internet connection to start up.
Once the camera starts up, connects to internet, authenticates with Wyze, obtains network time via NTP, (and transmits who know what personal and private information), it will then start recording to SDcard if that’s how you configured it. The internet connection can then be removed – the camera will continue to record. Until it loses power.
There’s lots of information on the topic of off-line recording in this thread.