I'm helping someone reset the password for her Apple Account so she can update her iPhone 12, which is running iOS 16.1.1. It's her only Apple device, and she has access to the Gmail address associated with the account. However, the password-reset option isn't visible in Settings, and starting the process through Safari asks her to verify the trusted phone number, which is the number assigned to the iPhone. The problem is that her carrier has no service at the locations where we're trying to do this. Would Apple send the verification code through iMessage or another internet-based method, or does she need cellular service to receive it?
2 Answers
On supported iOS versions, the option is usually under the Apple Account name at the top of Settings, then Password & Security. If the name section opens but there’s no password option, the older iOS version or the account’s security setup may be why it isn’t appearing. Updating iOS could make the newer recovery options available, but the existing trusted-number verification may still be required.
The verification code is normally sent to the trusted number by SMS or an automated phone call. It isn’t delivered through iMessage, so Wi-Fi by itself generally won’t help if the phone can’t connect to the carrier’s network. You’ll likely need to get somewhere with service or use another available trusted-number method.

That also explains why having access to the account’s Gmail address may not be enough—the trusted phone number is still required for two-factor verification.