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Not saying it can't be done but extra work and/or shorter lifespan are the caveats. I looked in to composite joists but even they need ventilation.
I missed that there appears to be patio on the other side in that pic so maybe there's is cross ventilation but I guess it's a good case study for why you need a clear line from either side and can't rely on the air circulating around closed corners.
From what I could tell when I was looking into building a sunken deck, the design is pretty much flawed due to the lack of cross ventilation. Even 'ground level' decks tend to be actually build from the ground level up, so 150mm or so finished level and I think it's generally accepted that they have a shorter lifespan. I can see yours* is probably raised on one side but closed off on most of the perimeter, so effectively no ventilation.
I was concocting a plan for a sunken deck with ventilation piped in from a cowled tube or two, but it seemed quite complex so we filled in the hole and sold the house.
*Edit: not yours