passport/n600 with expired green card?

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My child entered the country legally and has a immigrant visa in her passport which has now expired. She never received a physical green card. I thought it wasn't important because her mother is a US citizen and my child would automatically acquire citizenship upon entering the country. She was born after we got married and my wife is a citizen by birth, just didn't live long enough in the country to confer the citizenship automatically to our child born outside the US.

 

Now that I need her to get a social security number for tax purposes, I was wondering whether to apply for a certificate of citizenship through the N600 or a passport to help her get a social security card. For that process, do I first need to get an unexpired green card? Technically, the stamp in her passport's immigrant visa serves as proof that she has legally entered the country as a legal permanent resident, which should be enough to prove her claim to citizenship. Is this correct? Will I be able to get her a passport / CoC with the expired passport's immigrant visa?

[Andrea&Henry 311]

You as US citizen should report the birth of a child at the local US embassy to get a birth certificate/us passport. 

 

Did your wife at least registered the birth?

 

either way, your wife has to claim the child to begin the process.

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The child was born before we knew that we'd move to the US and didn't have a claim to citizenship at that time. That's why we never registered the birth.

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What do you mean by claim the child?