I have had the same problem when I factory reset my Macbook Air to macos 10.9, but as I had an iPhone Apple was still asking me if I would allow me to log in, although the device was saying the password was wrong. So I learned that it says, that you have to put your password followed by code they give you. Example: *******123456. That did work. I don't know if it should work without another Apple device.
PeterFence
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