You would probably need to be the US military. Once you have a setup onsite; helicopters, pilots, fuel, maintenance, crew to rig containers, you could rapidly unload the containers. Check out this video: https://www.youtube.com/watch?v=08K_aEajzNA
US Military is probably the only entity that could pull this off in a timely manner. At great cost of course...
Looks like your right. The US has:
https://en.wikipedia.org/wiki/Sikorsky_CH-53E_Super_Stallion... as its near equivalent with a external payload of 36,000 lb. The Russian helicopter carries 8000lbs more at 44,000lb, though Wikipedia doesn't say if this is an external or internal payload.
Looks like a 40ft shipping container weights around 8000lbs empty, couldn't find a stat on full. It seems such an operation would be outside the capacity of these helicopters. Sure they could comfortably lift empty containers, but probably not full ones.
US Military is probably the only entity that could pull this off in a timely manner. At great cost of course...