Used is the way to go
Picking up a bike that is 5 years old that was $2000 new for 3-500 is not uncommon in my area. Shop Craigslist or Facebook. This will be much better than buying a $500 new bike- no comparison.
Take her along and look for someone who is a serious mountain biker who is upgrading. Some folks have to have the latest thing every few years and there are some great deals to be had. You won’t find many dishonest bikers in my experience, especially is they know the bike is going to a kid. I have probably bought 10 bikes worth $2-5000 each for the kids over the years and never been burned.
I am partial to specialized, but there are lots of good brands out there. Google whatever you find and see what the original price was. You are basically paying for lighter weight and better components. If you get something that retailed for $2000 to begin with and doesn’t have any issues it doesn’t really matter much what the brand is, you are going to get a good bike with decent components.
ETA. I should have asked how old she is. If she is very young, the above doesn’t apply, obviously. If she is 10 or older you likely can find a used bike from a small woman that she can grow into. Don’t go too big too soon, or she will be handicapped and might get frustrated.