The second attachment worked, well done.
That's a delayed record of birth, there's (abt) a 6 year difference between the date of birth and issue of the record.
Unless someone comes along here and has some knowledge of birth records in Cook, ie, filing at the time of birth, changes, etc, then I would give the Cook County board a go. This is a question that needs to be answered.
The blather in the post below this one should be ignored. The board admin removed several responses refuting the unqualified assertions.