So, I talked to an engineer for a neighboring SoCal city...

He said there's typically a grading and demolition permit needed, structural engineer needs to sign off on the integrity of the pit, earthquake assessment, Dig Alert for utilities etc. But because he's Musk, SpaceX likely gets fast tracked for permits from the city of Hawthorne.

Found some details on the nitty gritty of it: http://www.dailynews.com/business/20170130/elon-musks-tunnel...