There's an explanation for Harvey's existence with the origin. According to Elwood, he's "a benign but mischievous creature from Celtic mythology who is especially fond of social outcasts." And Elwood is about as much of an outcast as the definition outlines, due to his inability to adhere to the social conventions that are demanded upon him by his well meaning sisters. Even if Elwood isn't normal, what is the harm in him befriending an invisible friend so long as he doesn't hurt anyone or himself? And really, what is normal, when we step back and examine it. Much of Harvey's existence is left ambiguous for much of the film, save for Elwood's explanation that he has the ability to stop time. This grants him the gift of all the time in the world, where Elwood hints at many journeys with his friend.
Of course since Harvey is a seemingly non-existent entity that Elwood regards with much respect, no one can really be sure if this magic is all Elwood's enthusiastic beliefs or if there is actually something supernatural at play. Harvey for the most part seems to be a being that exists mainly on influence of Elwood. And Elwood lives his life influencing others on the riches of friendship and being a kind human being, a trait that opens him up to heart ache. Jimmy Stewart is about as excellent as ever as this big hearted gentleman who only seeks to live his life as much as he can and do so with his rabbit friend Harvey at his side. Ultimately it doesn't matter if the six foot rabbit exists. It just matters that we can be ourselves and live our lives how we want to, so long as no one else is hurt in the process