ᐅ Materials for Sealing Joints Between Stairs and Walls, Soundproofing?

Hello, we recently moved into a house built in 2012, which has three fully enclosed concrete staircases connecting the floors. We have noticed that the house is extremely noisy, especially between the floors despite the concrete ceilings and enclosed staircases. This is because the staircases are not properly sealed to the walls; on the lower floor, you can even see light through the gaps at the sides into the floor above. My question is: what is the best way to seal these cavities? My father suggested using expanding foam, but does that effectively reduce noise? Once you spray foam into a gap, you can’t remove it... I would appreciate advice on which material should be used for sealing. Silicone probably won’t work, as the gaps are several centimeters (inches) wide in some places. Thank you very much for your assessment.