Hi Lukeappleiphone,
The account recovery process is used when no other method of regaining access to your account is possible. Per the article If you forgot your Apple ID password "If you don't have a trusted device, you can reset your password on the web — but the process might take a little longer."(emphasis added)
The page How to use account recovery when you can’t reset your Apple ID password further offers these suggestions on the process as well as how to check the status of your request:
"After you start account recovery
After you request account recovery, you get an email with a confirmation of your request and the date and time of when you can expect to regain access. This email arrives within 72 hours.
- If you submitted your account recovery request with iforgot.apple.com through your device's browser, you should avoid using that device during this period. Using that device might cancel account recovery.
- To avoid delays, turn off other devices that are signed in with your Apple ID until account recovery is complete.
When the wait period is over, Apple sends you a text or automated phone call with instructions to regain access to your account. Follow the instructions to immediately regain access to your Apple ID.
In some cases, you might be able to speed up the account recovery process or reset your password immediately by verifying a six-digit code sent to your primary email address. You might also be able to shorten the wait time by providing credit-card details to confirm your identity. If you’re given this option, an authorization request goes to the card issuer.*
Check the status of your request
At any time, you can see how long it will be until your account is ready for recovery, or when more information will be available. Just go to iforgot.apple.com and enter your Apple ID."
Regards.