According to the article, you don't need a permit to dig on your own property. He's going through the process you describe for when he hits the property line.
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.
