It's not just that their musical stylings are a match (though they are, and we can totally see Charlie jamming out with Andy, Kevin, and Daryl in their warehouse band sessions.) It's that Charlie is sweet enough to eventually be loved by the staff of Dunder Mifflin, even if he has to endure a few side-eyes from Jim for not being able to read or loving "milk steak" too much.
How it would happen:
The gang finally finds a way to send Charlie over the edge. It doesn't matter how. Maybe Mac zaps him by peeing into an open electrical socket that Charlie is attempting to fix, or maybe Dennis just mocks him one too many times. The point is Charlie quits Paddy's and treks up north to find a place of business where he'll be appreciated. Scranton is about two hours away from Philly, so it's about where Charlie could expect to land as he runs out of gas or his car breaks down. He then finds himself at Dunder Mifflin, but because Charlie struggles with literacy, he thinks they sell mufflers. One strange conversation with Michael Scott later, in which Charlie strangles a rat in front of Michaels's eyes, he's got himself a job doing the work that Michael would never, ever want to do. Charlie fits in beautifully, but he never does figure out where they keep the mufflers.