Very risky, especially with a newer arrangement.
What exactly is she asking for:
1. Buy her a new car outright out of your pocket?
2. Give her a significant amount of cash to buy it?
3. Give her enough cash to make a significant down payment, and then,
4. Help her make, or completely pay her monthly finance payment?
5. At what point will she deliver her new activities: Before the purchase, during the finance period, after purchase is compete (title is clean)?
6. Who will "own" the car, who's name will be on the pink slip?
7. Who will get and pay for car insurance (new car = Full comprehensive insurance in California)?
The answers to these will help you figure out what, if anything, you will do. But a few general issues to contemplate:
1. Title in your name technically means you can take back possession of the car at any time. BUT: If she crashes, damages property or persons you may be on the hook for liability.
2. Similar issue with insurance: In her name or yours with her as an additional driver. If she fails to make the monthly payment, you will need to make it.
3. Same issue with monthly car payments. If she defaults, you may need to make missed (and future) payments.
Some possible scenarios:
1. You finance or purchase the car - title in your name. She agrees to make monthly "payments" in cash or services. Risk: if you break up, you are stuck with an extra car and all future payments.
2. You fund the purchase or finance - title in her name. She agrees to make the payments on finance and insurance, or you make the payments if service delivered. Risk: She can bail any time before the loan is paid and you get stuck with the loan balance and without owning the car. Additional risk, she may miss dates or not honor you schedule (3 times a week may slip to 1 or 2).
3. You give her enough cash to finance - title in her name. The rest is up to her, but she delivers service immediately. Lowest risk (the initial "gift", but no ongoing payments or liability).
4. Same as 3, but you give her more than the down payment, up to the full price. Bigger risk than 3, but lower than #1 or #2.
My recommendation (without knowing any additional specifics): Stay away from owning the car and from signing up for loans (primary or co-signer) and from insurance. Instead, stick with giving her cash at some level and let her take on all ownership obligations. It will give her valuable experience, build her credit score and keep you out of the shit if (when!) it hits the fan.
In addition, I suggest that once she determines what make/model/year she wants to get, you offer to go with her to the dealer and lead the negotiations on her behalf. That again helps her gain experience and get all those warm-fuzzies from her SD who is wise, loving and caring. Plus, you can ensure she does not get "sold" on useless add-ons like under carriage coatings, spoilers, expensive tires or wheels, and no-value extended warrantees (these are primary dealer profit products). You can also help her navigate the insurance coverage bond and prevent them from selling her those bullshit over-prices 30-day insurance plans (that are added to the financed balance).
This way, your risk is limited to the one-time cash outlay. Remember that even if she "agrees" to sign some kind of contract between you are her, it won't be legally binding, and she can blow it off (as opposed to blowing you) at any time with zero consequences.
Of course, there are any number of hybrid deals you can propose... I had an SB in 2017 who had an ongoing "deal" with her last SD when we met, though she didn't tell me about it for a year. The last SD owned a used car business. He let her have a shitty car off the lot at a "discounted" price. Every week, she could either make a cash payment of $200 or a BCD payment. When she finally told me about the deal, she asked me to "buy out" the contract for $1,200 *. I took the risk and funded the buy out with her promise to make the weekly BCD payment to me. And yeah... she ended up stretching those to bi-weekly (heavy work schedule, or other excuses), then every three weeks until 12 BCD's were completed.
* Yeah, the math means she banged this guy 52 times while she was dating me! We had not agreed to exclusivity. I was perfectly ok with her having other SD's or banging the occasional hook up. Sill, 52 times! Maybe I'm not as well-adjusted to polyamory as I'd like to think. LOL And she told me this guy was a total slime bucket and since he was a used car dealer, that seemed credible.
Looking forward to seeing how this plays out.
Life is good
The Cat