Max G. is first mentioned in Wonder when August invites his entire English class to his birthday party, which includes him. Along with Max W, Reid, Jack, Summer, and Christopher, Max attends Auggie's birthday party at the bowling alley.
After Jack and August's fight, Max G. and Max W invite August to play Dungeons and Dragons with them at recess, an offer which Auggie accepts a couple of times.
When most of the boys are ignoring Jack, Max does not. He is on Jack's side, despite most of the boys initially being on Julian's side.
At the graduation reception, Max joins August and many other students in pictures that their parents take of them.