Hi,
I'm a French citizen, I used to live in the UK until April 2011 and my case seems close enough. My partner is an Argentine lady (we're not married) and our son was born in 2010.
In my case it happened as follows :
- I requested a turno at the consulate in London.
- I had to provide my translated and apostilled birth certificate and a UK police record (since I had been a resident for the last few years), also translated. The consulate already had my child's details (partida de nacimiento, DNI etc..) because he had been registered at the embassy in 2010 and had received a DNI.
- 3 days after my turno (during which I handed in my passport, and was interviewed by the vice-consul) I came back and collected my passport and visa, along with the "sobre consular" and, if I remember well, another envelope for migraciones.
- I arrived in Argentina in May and handed the 2nd envelope to migraciones, and paid the entry fee.
- I requested a turno to apply for the DNI once in the country. during that turno I left the "sobre consular". the DNI took about 6 weeks to arrive.
Now I'm not sure how it would play in your case if your baby does not have a DNI, I would suggest you approach the consulate in the US and register the baby so that he has a partida de nacimiento from Argentina. Maybe you can have the DNI done, in any case you will need them to know about your child. Once they do, you will be granted a permanent visa as the father of an Argentine citizen.
Et voila !
Ivan.