There are certain things that we haven't – and perhaps can't – "prove" as scientists. However, we are also unable to come up with alternatives. So, for now, the following things are "true":
Most scientists believe that the brain, as a biological entity, must have evolved. Thus, certain properties of our brains (and thus our minds) are likely the result of evolutionary pressures. Some (including yours truly, but not many cognitive neuroscientists) take this as a reasonable argument for the premise that the principle job of the mind is to adaptively interact with our environment (this last phrase is adapted from Cisek and Kalaska, 2010).
During a talk by Mick Rugg, he presented the Engram theory as the only one we've come up with yet. The idea is that the reinstantiation of a memory must be, in some part, a reinstantiation of the neural patterns of activity that were present at the time of the remembered material.