You can never prove with absolutely 100% certainly that something does NOT exist. You can only prove with certainty that something DOES exist. That is why the burden of evidence is to the person who claims the existence of something.
However, what you can do to a certain extent, is prove that the existence of something is extremely unlikely and/or irrelevant, because no one has been able to prove it’s existence.
And really… Science has researched some many aspects of this world, discovered so much about it’s working. And NOTHING has ever come up that hits at the existence of a god.
As far as proven that something doesn’t exists, this is the closest you can get!
Does that fact change the life of people? Well… not directly. After all, there wasn’t any direct influence of their religion in their life anyway, so removing god from the picture, will not change their life at all.