According to the American Bankers Association, $205 Billion of the $350 PPP loans have been processed through 4400 lenders as of Sunday, April 12, 2020.

https://infogram.com/ppp-program-1hxr4zqjeen54yo

For a larger perspective on the PPP loan process see this article in Entrepreneur Magazine which is also a source for the above data. Ir explains some of the SBA’s approval processes.