Hello Kristy,
This event can happen for several reasons. Since you are sure that your phone or mobile network does not block messages from unknown senders, it might be due to the fact that your phone is not getting recognized by the Microsoft System. I would suggest you continue trying to ask for the verification code once every 24 hours (if you do that more often, your account might get blocked due to unusual activity).
It's also proposed to clear your browser's history from cache if that's what blocking the process. Alternatively, you can open a new private window on your browser and try the whole process again (Ctrl + Shift + P).
If these did not work for you, I would recommend you filling the Microsoft Account recovery form here: https://support.microsoft.com/en-us/account-bil... . Since only the user can recover their account due to privacy concerns.
Feel free to also check out these two sources for the issue:
- https://support.microsoft.com/en-us/account-bil...
- https://support.microsoft.com/en-us/account-bil...