This answer will vary depending upon the person. Some people may see it sooner and some may see it later.
When I first read this story, I was suspicious very early on. The reason for this was Laurie's bad behavior. The way Laurie behaved to his parents showed that he himself was a pretty bad kid. For example, the "look up, look down" incident might show you that Laurie is not very respectful to authority figures.
The point in the story where every reader knows Laurie is lying is the very end. At this point it becomes quite clear. Laurie has been talking about Charles all this time and there is no Charles. Therefore Laurie is not telling the truth.