I married an Argentine while in the US. We had a child there. Before moving to BA, we (my daughter and I) applied for and received permanent residency through the Embajada in Washington, DC. (We lived just a few blocks away which made it easier.) They required all of the things listed in various places here (all translated/apostilled). It didn't take that long after we had everything. Took about an hour or so finally at the Embajada to fill the final forms, take fingerprints, stamp the permanent visa in our passports, etc. and then they gave us two sealed envelopes each (sort of mysterious!). The first was to be left at immigration at the airport (which it was, I believe this made its way to Migraciones eventually). The second was to be handed to Registro when we applied for our DNI. When we went to Registro, the woman opened them both (my daughter's and mine) up, pulled out the papers, and said (in Spanish and in classic Argentine style), "let's see what you're missing!". She sent us back for the official local translations and stamp by the translation office. She said we didn't need the marriage license, which I interpreted to mean for a DNI, it is only needed for permanent residency. And we also had to got to Migraciones and get our residency certified (Certificado de Residencia), which is essentially Argentina saying that their own Embassy stamped our passports correctly(!). (*)
Once I had the Certificado de Residencia, I went to ANSES to get a CUIL. They rejected me, since I didn't have a DNI. I had a lawyer with me arguing up the chain to what was supposed to be the head of that office that there was no reason that I had to have a DNI to get a CUIL. In the end, it was easier to just have the DNI in process, i.e. essentially got my appointment, and then went back to ANSES and got my DNI in a matter of about 5 minutes.
Soon after, since I wanted to register as a self-employed taxpayer (monotributista) to do consulting work locally, I went to AFIP and registered there quite easily for my CUIT (US equivalent: Employer Identification Number), 30 minutes in and out, although I had an accountant do the initial computer setup after getting the login information from AFIP, as it is confusing unless your spanish is *very* good.
Both the CUIL and the CUIT, without a DNI, have the same generated number that looks like a DNI number. Once you get your real DNI, you're to go back to ANSES (with photocopies!) and get that number put on your CUIL.
This all was just *my* experience of course. Others have had different ones. I believe that conversations during this process indicated that it *might* have been easier to get the CUIL if I hadn't received my permanent residency before arriving. I don't necessarily see/know how, but that might explain some of the differences. Or it might not!
Dennis
(*) Longer story for me was that we weren't too impressed by the Embajada in Washington, and they ended up costing me lots of headaches as the didn't put us in the computer like they were supposed to, so I had to go to the Cancilleria (equivalent to US State Department who is in charge of all Argentine embajadas around the world) who "kicked" the embajada in Washington into putting our information into the computer, but then the put my entrance date in wrong (on purpose?), so it didn't match the date on my passport. And that date entered into the computer "cannot" be changed by anyone, so I now have a stamped letter from the Cancilleria that says that the date in the computer is wrong and that the date on my passport is correct... This whole process took about 3 trips each to Migraciones and the Cancilleria. Luckily for me, we live near Retiro, so I could walk to both places. The Cancilleria is the modern glass building across Esmeralda from the old Cancilleria, which is the Palacio San Martin, the very beautiful palace adjacent to Plaza San Martin on Arenales Y Esmeralda facing Av. Sante Fe.
