"Too many codes were sent" on the first try in SMS login

Hi. I'm in need of some advice. My mother has been having trouble accessing her iCloud account. Her iPhone broke down, which means she can't log in, and to make things worse, the phone number tied to her account is lost.

I followed the recovery instructions and managed to update the number to mine. But a month later, when I tried to sign in, Apple kept sending the authentication code to her dead phone. When I requested an SMS code instead, I got an error saying too many codes had been sent and to try again later. It happened on the first try.

Could you help me restore access?

Many thanks.