How do fix my New MacBook Air? (not logged in)

You can forego migration & just create a new macOS account on the new Mac (just use defaults for everything & no need to use your AppleID/iCloud yet). Update macOS. Then after the update has been applied, perform an "Erase All Content & Settings" which will remove the current macOS user account, but leaves macOS untouched & allow you to go through Setup Assistant again like it did right out of the box so you can migrate from your Time Machine backup. The "Erase All Content & Settings" is very quick.

Erase your Mac and reset it to factory settings - Apple Support

"How do fix my New MacBook Air? (not logged in): I just got a new MacBook AIR and I have been trying to migrate my data from my MacMini to it and my New MacBook is saying that it is an update behind my MacMini??? How do I update it without logging in??? Is there a way to 'un-update' my MacMini??? Help!"

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Updating a NEW Mac:

How exactly is this "New"? Is this Mac new, and out-of-the-box? Or is it a previously-owned Mac that is new to you? And what is the model? Identify your Mac mini model - Apple Support. If older, then it may be incompatible with a newer macOS version.

IMPORTANT: Be certain you create a Time Machine Backup of your Mac prior to making any major change to it, whatsoever. That way you can have something to restore it from, should anything go working afterwards.

Updating an Out-of the-Box Mac:

Update macOS on Mac - Apple Support

Updating a Previously-Owned Mac:

If used, and you cannot log in, then the prior user needs to log out of iCloud on it, and reset it to Factory Settings. This I the site the sell should have used, prior to selling it to you: What to do Before you Sell, Give Away, Trade in, or Recycle your Mac - Apple Support