If I understand the question correctly, your site has several lists and libraries. You want to create a site group that has access to only one of the libraries. You’d like to know the easiest way to create the group and deny access to all but one library. Is that correct?
When you create the new site group, give View Pages as the only site right. Do not give the group the View Items right. The group then has access to the site, but not to any lists or libraries. Then go into the one document library where you want to give access, and change the permissions setting for that library to give the group access.
This still breaks the permissions inheritance, so any further changes to the global site permissions after the fact will not be picked up by the one doc lib. But it will at least save you a few steps in your set up.