Insulating floor of cantilevered fireplace

Looks like the small floor of our cantilevered fireplace was not air sealed or insulated. What’s the best way to do this? We will be doing the work from the outside of the home.
Spray foam isn’t an option unless we’re talking about using the cans.
The floor joists extend into the basement and the rim joist from the basement side were covered with close cell spray foam.
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Funny, I was just at a building investigation yesterday with the same condition. From the photo, I cannot tell if the underside of the cantilever is open, but I would assume there is at least a plywood covering.
Here's a detail by Alexandra Baczek covering one way to complete the assembly:
https://www.greenbuildingadvisor.com/article/positioning-control-layers-in-a-cantilevered-floor
What I'm going to be suggesting to the customers from my building investigation is to seal all joints between the conditioned space and the cantilever using a quality sealant or some sort of canned foam that creates an equivalent air barrier, insulate with fibrous insulation, and cover the bottom with plywood that is also sealed using a caulk or sealant. If you have enough space, a piece of rigid insulation could also be added between the cantilever and plywood covering.
Hope this helps,
Randy
Thanks Randy.
If you're using rigid foam between the cantilever and plywood covering, what is the best way to secure the foam board into place? Construction adhesive to the floor joists? Screws?
Should the fiberglass batts be faced or unfaced?
If you are going to use an adhesive, it needs to be rated for foam insulations, solvent based adhesives will eat foam. A cap nail or screw might be better. If you use a faced fiberglass batt, the paper usually needs to face the warm side or inside of the assembly.
What sealant do you recommend to air seal all the joints?