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Regardless of where the stair is located, you need to use conventional framing for the stair opening. 1-3/4"x "depth of floor" LVL's would be best at framing the opening, since they are stronger than the typical 2x's; they should span the same length as the the truss joist when running in the same direction. The joists parallel to the stair should be doubled and so should the headers. Everything should be held together with metal joist/ beam hangers and the truss joists can end at the headers, to be held up with metal hangers. No posts are needed. Here is an example of a framed stair opening, except I would use doubles around the entire perimeter, and these would be solid wood. The rest of the framing would be the open trusses.
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Best of Luck, Brian
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Sorry, I didn't realize that the trusses were spanning 32 feet and that they are 24 inches deep......these are larger than typical framing. LVL's may come that deep but it is not worth getting them 32 feet long and 24 inches deep.....they would way a ton and it is not economical.
I would put in (2) 3" steel round columns, if you can, to help support the opening; these should sit on a thicker concrete footing and not just the concrete slab. I would still frame the opening with LVL's.....(2) 1 3/4"x 11 7/8"; these would sit on the foundation wall and the two columns. The truss joists can then attach to LVL's with joist hangers. The 3/4" OSB subfloor is adequate for spanning 16"o.c. Here is a diagram that I drew, based on what I imagined you were saying.