If there's really nothing to attach it to, you could rip the box out and use a rework box, like this:
https://www2.lowes.ca/product/electr...-clamps-264428
They're designed to mount only to the finished surface, though you'd need to find one that A) fits your cutout; and B) is large enough to fit the GFCI outlet you have there.
You'll find more options at an electrical supplier:
https://ebhorsman.com/category-items.php?cat=581212
I've bought things from them before without being an electrician or having an account.