Approve a device without having another Apple device

I have a company MacBook Pro, so I am a little bit restricted in administration setting.

By the way, I need to access iCloud, that was created with the previous MacBook Pro (changed some weeks ago) and where there are important documents that I would like to sync with this new one.

The problem is that when I try to sync iCloud it is asking for the Apple ID login, the iCloud login and then to go to another device signed in to iCloud and approve this device.

Now, if I log in to iCloud, and also Apple ID, I can only see this new device registered in both my accounts, as the old MacBook was previously removed as no more used.

I have already tried to remove this new MacBook to have no device registered in any of the accounts (iCloud and Apple ID) and tried again the procedure. Correctly, when logging in, I am receiving the SMS with the code to my phone (not Apple) for the 2FA, but then the procedure tells me every time to go to another device signed in to iCloud and approve the current MacBook. Only at this point, in both the accounts, I can see that this new MacBook has been added again to the devices section.

As you can imagine, I do not have any other Apple device to approve this new MacBook and the solution proposed else where in this website, are not helpful because they suppose you have another Apple device or they just say what I have already tried and wrote above.

Is there anything that I can try about that?

This is an iCloud keychain prompt. In order to allow you to sign in to the Mac, you'll need to approve it. If you only have one device on the account then you must have had another apple device in the past that you used to set up keychain. Often times some users will turn keychain on and then realize they don't know what it is or what it does so they turn it off. The moment its turned on, you activate it and it identifies itself with your Apple ID.

If you don't care about iCloud Keychain, the screen should get you an option to reset iCloud Keychain. It should say "Can't approve from another device". Once you click on that, next it will say "If you can’t approve this Mac from another device, you can reset your end-to-end encrypted data to finish setting up iCloud". That data is your keychain passwords, wifi passwords, Messages saved in iCloud and credit card numbers (more info below). If you don't care that it will erase that information from your account, then have it reset the keychain and it will allow you to continue to the phone setup.

iCloud keychain is a secure management feature that keeps your account names, passwords, Messages in iCloud and even credit card numbers stored behind 256-bit AES encryption on Apple's iCloud servers. Then that data is synced between authorized iOS/iPadOS devices and macOS devices.