AS SOON AS POSSIBLE! The earlier you can involve your staircase designer the better. Why?
To create enough room to make a natural and comfortable staircase. I have often been involved in the final placing of walls, and marking out the size of openings. It is a real shame to fit a staircase and find that the headroom is restricted or there is not enough room for a natural feeling handrail.
To ensure that the structural components needed to fix the stairs to the building are in the right place. With a bespoke design, the structural details can be different from what your architect and builder are used to, I like to build a rapport with all the trades on site early in the build. For example, in some cases it might make sense to build some plywood in behind the plasterboard to provide solid walls for fixing, or I might need a very precise curve to a wall.
To make sure that there is no electrics or pipework in the way of fixing the stairs. In particular where there is underfloor heating, I like to ask the plumber to leave an area clear of pipes at the foot of the stair so I can fix down easily.
To allow time to manufacture the stairs in advance of when it is needed. With a timber staircase, I like to install as late as possible. There is nothing sadder than putting in the staircase then finding it covered in plaster! Whilst it is nice for the builder to have a staircase in place, the worry is that they use it!
Having said to involve a designer as soon as possible, I once had a very long conversation with a self builder about a staircase, he had architects drawings, and was very sure about what he wanted, only to discover that he had not yet found a building plot!