I doubt it would be possible for the night-shift supervisor to bring the noise down, since these constructions are on a tight schedule and needs to be completed early on. Alternately try putting some heavy curtains. I understand what you're going thru, as right now, I am sitting in my office next to a construction site, and taking in all the noise. Search for a noise-cancelling device, like shown in the below website:
http://www.audiosmarter.com/top-noise-cancelling-sound-machines/