Hi, Chris,
The gating item for most people is the criminal background check for each of you from your home government, because it has to be less than 90 days old when you present it to request permanent residency. It also needs to be apostilled by the South African authorities, and translated into Portuguese by a sworn translator in Brazil. All South African documents that you present, except for your passports, will require apostilles and sworn translations. (Fortunately, you can arrange for the translations online, even before you leave South Africa, and they don't expire.) So, you need to balance the time required to get the Background Checks, get your and your wife's other documents together, and get the apostilles, against your baby's anticipated due date, to work out when it's best for you to arrive in Brazil. Your VIVIS visa should be good for 90 days, and you should be able to extend it for another 90 days. Once your application for permanent residency has been accepted, the clock stops on your visa while your application is processed, so you SHOULD be able to avoid visa problems with some basic planning.
You should be able to request and obtain a Birth Certificate within days (maybe even hours) of your child's birth. Many maternity hospitals have a cartório -- a notary or registry office -- onsite; if not, there will be one nearby. You'll need a Declaration of Live Birth (DNV) from the hospital, your and your wife's identity documents, and maybe, your marriage certificate.  As with any official Brazilian document, I recommend investing in duplicate originals ("2a via") when available. Once you have the Birth Certificate in hand, you and your wife can go to the Federal Police and request permanent residency.
The ID card for expat permanent residents is now called the CRNM, Carteira de Registro Nacional Migratório; it used to be called the CIE, and most expats called it the RNE -- all the same thing. The list of documents required for permanent residency -- is on the PolÃcia Federal website, here:
Check it frequently, because it sometimes changes as regulations do. You'll want "family reunion", "reunião familiar", by virtue of having a Brazilian child. Not every document requirement on the list will apply to you.
After accepting your application, the Federal Police will tell you that your CRNMs can take up to three months to be issued. This is probably true, but I had mine in a month, and most people report getting them in about that time, except at the end of 2017, when all the rules changed and the system slowed down, until the new rules were understood.
The normal wait time for naturalization is four years, but it's shortened to one year in cases of family reunion. So, one year after the issue date of your CRNM (and NOT of either your arrival in Brazil, or your child's birth), you can apply for naturalization. This is also handled by the Federal Police.
Documents required for naturalization:
I haven't done this process yet: I'll be starting it in November. People who have done it here say that, even after your application is accepted, it takes months and months for it to be approved.
Thanks for cluing me in on the concept of "powerful" passports -- I had not run across that before.Â
Question for you. As much as I love Brazil, I'm a little surprised that it's your choice. Sounds like you and your girlfriend might have the skill sets that could get you into Australia or Canada -- wouldn't either of them be an easier proposition all the way around?