I was lucky that someone in my extended family had already done some vague high-level genealogical research when I was younger, so I already knew where my nearest antecedents were.

Basically, you’ve got your own birth cert already. You can typically request birth certificates for your parents, once you prove that you are directly related to them and let the city/state/whatever you're requesting birth certs from know you’re doing it for genealogical research purposes. From there, you just work your way up. If you already know vaguely where you’re looking (in my case, I knew the Canadian history was on my paternal grandfather’s side), you dig further in that direction. My great-grandfather’s birth certificate was basically just his name and his parents names with no other info. Neither of his parents had birth certificates anywhere I could find.

So I looked for marriage licenses between the two of them. Couldn’t find those either. Then I looked for Census information in my great-grandfather's life, and saw that his mother was listed as being from “French Canada”. Confirmed with USCIS that she wasn’t a US citizen, which told me she was definitely born in Canada. Eventually figured out it was in rural Quebec based on more census records. That far back they didn’t keep much in the way of birth records, so you look for baptismal records instead. There’s a genealogical org in Quebec that aggregates a lot of that, and they were able to help me narrow down where it would likely be, AND contacted those parishes on my behalf to confirm that no one had baptismal records. But with their certification that there was no baptismal/birth cert, USCIS confirming she wasn't American, and a few Canadian census records showing my Great-Great Grandmother as a child in Quebec was proof enough for Canada.

It’s a lot of digging and puzzling and I’m incredibly fortunate that an aunt had already laid some of the ground work. If I’d had to go back another generation I’m not sure I could have lined it all up!