The simplest way is obviously to frame up walls directly around the future stair opening on a sill and place a so-called top plate over the top of the studs cut to fit snugly between the sill and the top plate. Then cut out the opening. A suitable dimension for the vertical studs (spacing 600) and the sill is 45x95. The top plate should be a 45 x145 on edge, which you embed in the top of the vertical studs so that it is flush directly.
The slightly more complicated option (if you don't want walls directly around the staircase) is to temporarily brace with a roughly equivalent structure directly around the staircase and then cut the three beams needed + 45 mm directly. Then use joist hangers at each end to create a header with 45 mm material that is the same height as the beams in the floor structure. But then you will have a problem connecting the cut beams to the header. It can certainly be solved with more joist hangers, but it becomes difficult to attach them as they will be located under the edge of the remaining floor/ceiling. You may also need support in the middle down to the floor directly since the length is 3 m.
Primarily, considering that there will be narrow passageways on each side of the stairs, I would try to move the future staircase to one side closer to a wall where support for the floor structure might already exist? and settle with a new wall on the opposite side of the stairs.
