Things going slower then you thought, prefer to be a safe site?  You can have your staircase water resistant so that in the construction process you can have safe access to the upper floors.  We dip the stringers in a stabilizing solution the treads and risers are made from a special birch ply we then use a waterproof glue and stainless screws to put it together. The stair is fitted as normal early in the development and it doesn’t matter if it gets wet.