Funny this comes up. 67Prince is in his first NICA season. He's dabbled in and out of all activities, each of the past few years he has gotten more into it. Bought him a used XS Liv full suspension for Christmas. It is heavy as heck, most of the NICA courses here don't need an FS bike, and he has gorwn a few inches, and put on 15 pounds since them. Was going to hand him down my M Giant Stance, but now that NICA is in the picture, that is is too heavy, too.
So I just bought him a cheap hardtail frame from AliExpress. I have an older hardtail I bought used a year or so ago to see what I thought of gravel. Open mold bike with good components. Ended up buying a Lauf for 67Queen, and rode the generic bike with her when we rode together. Otherwise, I swap seats on the Lauf and ride it (I'm pretty short, 5'7", and she is 5'6", so same size bike). At any rate, since I built a better XC bike (Fezzari) over the Winter, I don't need the generic one any more, I just ride my XC one. So I'm taking all the XT components and carbon wheels off of the generic frame and putting it on the smaller one. He'll ride it this year, but probably either ride the Fezzari of mine next year, or I may spring for a used FS XC bike for him, depending on how he takes to it.
I bought the Liv for $1000, but spent another couple hundred converting it to a 1X12, from a 2X. I had spent $1000 on the generic bike, then $300 on the frame. You may luck out, but it will be hard to find a good bike for $700. If you are comfortable with building bikes, I wouldn't rule out spending some money, and anticipating buying some frames as she grows, and just moving the good stuff over to the new frame.