As near as I can figure your best bet is to do whatever 'normal' people do to get their personal infomation into the mainstream financial networks databases.  Buy shit with plastic, stay at hotels, try to take out loans, sign up for a credit report, etc.  I'll probably take a few years

If you are not legit you might have your work cut out for you since it seems like these guys do run a fairly tight ship.

I don't mean to be nosy, and I don't even want an answer, but it strikes me as a funny use-case to have a need for immediate BTC.  Mostly because I don't have that need myself I suppose.  If you do have that need for some sort of business purpose, I guess you'd be best off to build your business and BTC reserves up over time then essentially be your own supplier for short-term needs.

As an aside, it is worth note that in Coinbase's verification process there is no need to have instant-buy.  It is NOT the same track as having a level-1 limit.  I specifically did NOT want to have instant anything in my use case since it puts me at risk but I did want a decent sized transaction limit.   It was not clear to me that instant-buy is easily avoided.