The fact that one has lived before this life becomes very clear after a person has had Scientology Auditing. How long it takes a person to recall some past-life experience varies depending on the individual. Of course, no one insists that a person recalls a previous existence, it just happens as part of increasing ones spiritual awareness.
Because the idea of having lived before has been suppressed in the western world for thousands of years, when people a past life they will usually shy away from the memory or think it is from a movie or something they dreamed up from a book they read. But despite this. it is possible to recall past-lives without auditing, and there have been numerous such cases in the past (such as the Bridey Murphy case). Where the idea hasn't been suppressed for so long, reincarnation is a common idea. For example, it is part of most eastern religions.
So when a young boy in the USA starts to remember his life and death as a pilot during WWII, it doesn't really surprise me, but perhaps it will be of interest to you. Here is the video:
Here is the link if the embedded player doesn't work: 11 year-old Boy Reincarnated