Oh I don’t doubt for a minute you can “get” the baby.
I question how you can “document” the baby.
Unless you live in the third world, or far from civilization, you’re gonna have to cough up documents required to prevent this specific thing.
Oh, I’m sure if you can get a baby, you can get documents. They’re much easier to produce than babies. After all, millions of “undocumented” people have documents.