If you’re on the sign-in page and can’t access your authentication app, click “I can’t use my app right now.” Then look for an option like “Show more verification methods” to see if you have a backup (e.g., a phone number or alternate email).
If you don’t have access to any of the options listed, select “I don’t have any of these.” This will begin the recovery process. As part of that process, Microsoft will let you add new contact information — but only after a 30-day waiting period.
This 30-day delay is intentional. It’s a security safeguard designed to protect users in case someone else tries to hijack their account by changing recovery info. The wait gives the rightful owner time to notice and stop unauthorized changes.
Unfortunately, this policy cannot be bypassed. You can read more about it directly from Microsoft here:
So if you need to use the computer right away your only option is clean install. Set up with a different account for now. Wait 30 days and link the old account back. However doing so you do lose all data unless they were already backed up somewhere such as OneDrive.