So parents/grandparents/great-grandparents are totally unknown to her, but she knows the identities of (some? all?) of her great-great-grandparents? If so, it might be helpful to explain how that is--- because we usually know about the relatives older generations tell stories about, and we have no clue about the relatives no one mentions. I wanted to build a family tree this summer, so I asked my maternal grandparents for names further back. Grandma had the set of Great-Grandparents down just fine (her parents), but was very wobbly on her grandparents' names (my great-great grandparents). I only got first names for the two wives, and a question mark on the first name of her paternal grandfather.
I had way better success on my maternal grandfather's side of the family, because we had some serious genealogical effort going in, and they had made a little book so that no one had to re-do all their work. But they were only focused on the male line, so the wives were dead-ends in and of themselves once you got into the 19th century... but the male line was traced back to c. 1500.
I ran into similar things when I was looking at my father's family. There had been a good deal of work done on his mother's line-- but again, the wives all seemed to come from nowhere, because they didn't overlap with anyone else's trees.
Everybody has sixteen great-great grandparents. So technically, her "distant relatives" would be all of the descendants of those sixteen individuals, as well as everyone else who happened to be siblings or cousins or aunts or uncles or whatever of those sixteen individuals, plus their offspring...
So, for plot purposes, I'm imagining that the focus of the trouble is only on one line within the family, traceable to descent from one particular individual? Like my father's father's father's father and his descendants? Or my mother's mother's mother's mother? Otherwise, it will easily grow into over a hundred people, depending on where you set your limits. (Are you including family members who aren't genetically related? Adoptees? Stepkids? Spouses?) Which makes it technically way easier to find someone, but it has less impact when you bump into someone you need a chart to understand the relationship.
She can come across a family Bible or an old diary or an old yearbook or a cemetery and use that for names/relationships, especially if there's an unusual surname in play.
She can go to the courthouse in the county she was born, and find out the names of her parents and use that as a starting point.
She can go to her public library, if it has a decent genealogy room, and an open subscription to one of the family tree sites. If, say, her second cousin (shares a common set of great-grandparents) was a big genealogy nut, much of the work might have already been plugged in.
Or she might have a basic idea of names and places, and might start communicating on FB, saying stuff like, "Hi, I don't know if anyone remembers so-and-so who used to own a grocery store in your town in the 1940's. Does he have any living descendants? I'm trying to track down my family tree, so any information would be appreciated." People like being helpful.
Once upon a time, I had a woman who had been given up for adoption by her mother, but the records were sealed. She knew that she had worked for a particular bank in our city in the early 70's, and was trying to find a way to find the employee rolls during that time period. (Wasn't able to help her.
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She might throw $x at a DNA test that's connected to a family tree website, like AncestryDNA or FamilyTreeDNA, and discover that she is unusually genetically matched with this family over here.
A lot of it depends on why she's isolated from her family history. If she was a war orphan who was sent to another country for her safety, it plays out differently than if her mom gave her up for adoption to avoid the stigma of being an unwed mother, but everyone's still probably within 100 miles of each other. If it's a fantasy story--- the variables can be even more complicated.