When I got mine (and the same when my wife got hers) in St. Charles county, I was at the DMV within 10 minutes and all was ready. Now, I know in St. Charles county, they use a phone message system for you to check when your permit is ready (by number when you apply) so it may have taken them a little while to get the info into the system and you may not have been notified that your permit was ready for anywhere from hours to days before you found out.
Seems as if all counties are different somewhere in this process. My wife's sister took her class with her in St. Peters, she lives in Cole County. Cole County actually calls you when your paperwork is ready.