Hello,
With the old account you are trying to access then delete, do you know if your old MacBook was the only trusted device you were signed into that account with? Mac’s, iPhone’s, iPad’s, iPod touch’s, and Apple Watch’s can all be trusted devices. If you have one of those, that is already signed in to the old account, charge it and turn it on. After the device is on it should be able to receive a code for you.
If you don’t have another device that used your old account, hopefully you added a trusted phone number which you can still receive text messages or calls with.
Get a verification code and sign in with two-factor authentication - Apple Support
"Get a text or phone call
If you don’t have a trusted device handy, you can have a verification code sent to your trusted phone number as a text message or phone call.
- Select “Didn’t Get a Code?” on the sign in screen.
- Choose to have the code sent to your trusted phone number.
- You’ll get a text message or phone call from Apple with your verification code. This text message might include an additional domain validation line. This line includes the @ symbol, the website name, and your code (for example: @icloud.com #123456 %apple.com)."
If that is also not possible you might be left with using the account recovery process.
How to use account recovery when you can’t reset your Apple Account password - Apple Support
"What is account recovery?
Account recovery is a process designed to get you back into your Apple Account when you don’t have enough information to reset your password. For security reasons, it might take several days or longer before you can use your account again. We know this delay is inconvenient, but it’s important so that we can keep your account and information safe.
Before you start the account recovery waiting period, try to reset your password on a trusted device.
Use account recovery only as a last resort when you can’t sign in or reset your Apple Account password any other way.
- If you don’t know which email address or phone number you use with Apple Account, try different email addresses or phone numbers. You can sign in and reset your password with any email addresses or phone numbers on file in your Apple Account.
- If you don’t have a trusted device, you can reset your password using the Apple Support app on a family member’s iPhone or iPad. You can also visit an Apple Store and ask to use a device on site.
- If you set up an account recovery contact, they can also help you reset your password."
I hope this helps.