What happens if you have a baby while on vacation?

[Aug2020gal]

Let's say you are a Canadian citizen (not by descent, so you can give Canadian citizenship to your baby) and you are in some country, say Brazil and you give birth. In order to return to Canada, I take it the baby would have to have a Canadian passport since it is a Canadian citizen. But the parents are only tourists in Brazil and their work is back home in Canada. Is there a different expedited process for getting newborns a passport or emergency document to return to Canada before the parents' lose their jobs or overstay in Brazil?

If one of the parents is a citizen of another country as well (say Australia) and that country has visa-free access to Canada and issues the newborn a passport very quickly, is it ok to come back to Canada on the Australian passport? Once back in Canada, the search for citizenship records can take its sweet time. What would the consequences be if the parents showed up to the immigration desk and explained that the baby is actually Canadian but doesn't have a Canadian passport and travelled to Canada on its Australian passport?

Basically, how screwed would the parents be? Would they need to stay in Brazil somehow for around a year until Canada takes its time to search for citizenship records? The Canada Embassy in Qatar website says newborns under 2 years of age don't need proof of citizenship themselves, but I was unable to find this exemption anywhere else.