Two-Step Verification even though its disabled w/ Google?

[Admiral Naismith]

I have Two-Step verification disabled for my google account. In fact, it's never been set up. Today, I tried to log into Nvidia's Geforce Experience on a different computer (a different google account was used at one point). I correctly used my pass, etc.. Google's sign in has prompted me to "Verify its you", and its forcing me to provide a phone number to receive a verification code. There is no way to continue without doing this that is apparent to me. Is there a way to disable this sort of thing from happening/continue without having a phone? Again, I don't want to ever have to use Two-Step with google right now, I've never used it before, and I don't particularly like that its asking for a phone number when I used the correct password. Tried to search for how to get around this, but all I can find is "how to disable Two-Step verification"; it is already disabled.

 

Also how is it secure to ask for a phone number when you suspect the person isn't who they say you are?  Couldn't an attacker or whatever just provide a burner phone number to receive the verification code? How does this really prove its who I am when it could be any phone number?

[LogicalDrm]

AFAIK Google has done that for a while now. You need either to give phone number or setup Authenticator service.

 

And AFAIK phone is verified first time with other verification things you have. Like secret questions or secondary email.