What do you mean by proof?
First of all, there is no such thing as proof that something is possible. Everything is possible until proven otherwise. (In fact, philosophers of science hold that science never proves anything; it only disproves theories until what is left might be true.)
I can say that I have proven, in my life and the life of my spiritual coaching clients, that it is beneficial for some people to believe that they have past lives, and to work with spiritual and emotional issues as if they do. When these issues are released through therapy that acknowledges past lives, profound healing and empowerment can occur.
In that sense, past lives are proven to exist at least as much as the common cold is!