The roof of the 10,000-seat venue, which will host gymnastics at the Olympics and boccia in the Paralympics, will be raised in 200-tonne sections with all five scheduled to be in place by May next year.
Construction at the venue is due to be completed by the end of October 2019 - in time for test events ahead of the summer showpiece.
Tokyo 2020 organisers said construction was right on track, even if they still felt a huge amount of pressure to deliver the venue on time.
"As you can see, if you look around, the construction work is progressing very speedily," said director of venue development Toshihiro Hosokawa.
"Next year, at the end of October, the centre will be completed so there is only a year to go, hence my mixed feelings."
The venue, located in the Ariake district of the Japanese capital that will host many other Olympic events, will be used as an exhibition centre when the Games are over.
However, it is only a temporary structure designed to be dismantled by 2030.
To make it easier for the materials to be recycled and also to showcase Japan's timber industry, the roof, which spans 90 metres, is made from local larch.
The head architect on the project, Hidemichi Takahashi, said sustainability was at the heart of the design.
"The design has a view on post-usage after the Games," he explained. "No major changes are needed for it to be used after the Games.
"From an eco-friendly point of view, this venue uses the most amount of wood out of all the Tokyo 2020 venues."
(Reporting by Jack Tarrant, editing by Nick Mulvenney)
