You cannot prove a negative–something that does not exist. Nor can you disprove a positive–something that does exist.
For those that are intellectually honest, its difficult to imagine the entire cosmos began on its own out of nothing. Furthermore, its difficult to account for at least 1 out countless potential solar systems out of countless galaxies within this 4 dimensional universe to have at least one planet to have precise conditions where life can not only exist but begin, evolve, and thrive on its own. Take a step further, it takes a lot of mental gymnastics to get to the point where unconscious life takes a leap to consciousness on its own. Not quite finished, it takes faith to believe through NATURAL selection alone consciousness can somehow become intelligent. I think someone with scientific understanding would say everything here is in reverse order.
Even if you can prove this mathematically, it would eliminate an important premise to the atheistic evolutionary model which states order out of chaos explains the present state of the universe. There is no math that demonstrates order out of chaos.
My conclusion from this is it takes more faith to believe in this scenario presented than it does to believe in an intelligent creator…