First, consider what you're trying to determine. Here are some suggestions:
- Is the player comfortable with the game, DM, and other players, enough to enjoy playing?
- Is the player comfortable with the basic rules?
- Is the player comfortable with the character's backstory?
- Is the player comfortable with the character's specific abilities?
- What notable events in the character's backstory inform their Ideals, Bonds, and Flaws?
- What is the character's place in the world?
- What is the character's place in the plot?
- What parts of the world don't the party usually see?
Fortunately, there's a great way to determine all of the above.
I suggest running a session that focuses on two or three formative events from this character's past.
It should be clear to everyone that nothing is being set in stone until the end of the session. What half-orc wizard? Of course her character has been a halfling barbarian the whole time. No idea who you're talking about. You can even start with blanks on her character sheet and fill them in as you go (particularly for Ideals, Bonds, and Flaws).
I wouldn't necessarily state it outright, but this is also a good way to trial run the game for her. If it turns out she doesn't like it, you can always declare the session null and void. No harm, no foul.
The people attending can (should!) be the whole party. There is no point in keeping secrets from them, though there may be a point to keeping secrets from their characters. This can also be a nice break for your normal weekly game (but get buy in from those players first!). If your player isn't comfortable with having everyone there, consider just one or two other players. I'd advise against one on one, because it can be very intimidating to new players to have the GM looking expectantly at you every few minutes while you draw a blank.
The other players, if any, can have some fun here as well. Let them try out one-off characters, whether as PCs or NPCs. This can be great fodder for bringing in new characters to your main story line. Note that their characters don't even need to be in any kind of party or relationship with the main character. A chance encounter of the same-place-at-the-same-time variety is enough. Maybe they're on the same side in a bar brawl, or got matched against each other in a tournament of some kind.
The goal is to answer as many of the opening questions as possible. The tool to do that is to run a session. To ease the player into things, try running a combat and a non-combat encounter at each of levels one, three, and five or six. The idea is to give her the one to N leveling experience in a condensed form. This is helped by the fact that it's her flashback session, so she should get half or more of the group's focus, as opposed to the 1/5 she can expect in a normal five player session.
You can skip level one if you think the player is comfortable enough with the bare basics. Level three is recommended because that's when most classes get their iconic and differentiating archetypes. Full casting classes also get second level spells, which is a good introduction to their resource management. Level five gets martial types an extra attack and casters third level spells. If the chosen class has a cool and exciting ability at level six, just go with it. That one level shouldn't make a big difference in combat or anything, and if it helps her get a feel for the class, then why not?
After each level, ask a quick question or two on how she's feeling about everything. If a the character made a big decision, or better yet had a strong instinctive reaction, take a look at the Ideals, Bonds, and Flaws. Remember, nothing in the character is set in stone yet, and it's totally fine to take a half hour or so to roll up a new character.
When you're done with the session, you can level up the character to be in line with the rest of the party. I'd suggest the lowest, but at your discretion you can put her at the average instead.
As mentioned above, this is a great way to answer a variety of questions about the character, like where that trinket or magic item came from, how they got a scar, or why they hate corn. It can also answer things like why they have a vendetta against Vile MacEvil-Visage or one of his henchmen.
Your job as DM is to have a good idea of how those encounters will work together to bring the character into an alliance with the party. Don't just have a generic goblin encounter here when the party is fighting a lich in the future.