If someone were to dig real deep, I think they could actually find some information leading them to come to the conclusion, that they have lived past lives. I have always been a believer in the idea of reincarnation. There actually was a time where I thought that was what happened to everyone.
By doing reincarnation research people will be able to document and scientifically study people who have supposed past life experience. If they are able to prove that some people have past life memories, it would be mean the possibilities of having a past life are real, not fully valid, but possibly real.
There is no way to prove something that is completely reliant on someone's memory. In fact, sometimes people only have past lives when they have been put under hypnosis, which puts them at a disadvantage logically, and makes them open to the power of suggestion. A person's core faith beliefs are just that, faith. There's no way to prove a faith.
I am going to have to say, no, they can probably not prove that people have had past lives. To this day, there hasn't been a real, credible piece of research that has led to any actual proof that any religious phenomenon was real and was created by the thing that the religious people have stated that it was.
There's really no way to prove that reincarnation exists. People who talk about experiencing it may have been led to believe so through hypnosis, power of suggestion, or other reasons. One of the things that makes faith beliefs faith, is that there really is no way to prove them. You can't really prove it through science and research.