The staging is supported by piles which go all the way down to (and beyond) slab level in the basement. The excavation will continue underneath the staging platform, around the support piles. Ultimately, the staging platform will be replaced by the at grade ground floor slab, and the support piles will be removed.
This process can probably best be seen in some of the photos in the Nobu Residences thread, where the staging platform was built at the west end of the site, and then once it was in place, the excavation continued beneath it. The time taken to do all this, including the slower and more labourious excavation process under the staging platform, is why the western portion of Nobu is nowhere near as advanced as the eastern portion of the site.