Squirrel or rat; and do I trap first or exclude first?
Get tin snips and a soup can.  Cut 'teeth' so that each tooth is about 1/6 of the circumferrence of the can and staple them points pointing toward each other, but spaced out a bit.  The curve should point away from the wall.  My first guess is that you should be able to slide a broom handle through the space between the teeth.  Your squirrels may vary, but they are smaller than you think.  Another estimate 3/4 of the size of the hole they carved.

The idea is that a squirrel can push the teeth aside to exit, but they jab when trying to enter.

Another method may be to tack a piece of hardware cloth with fence staples as a hinge.  In essence you are building a 1 way pet door. Tie a small weight to the bottom edge so that if fits fairly close.  This one may be opened by smart squirrels. 

You may want to run a microphone on a stick into the hole and see if you can hear inhabitants.