You can't disprove an abstract concept. You talk about one god, so you probably come from an abrahamic background. From those three islam and judaism were never that keen on clinging to denial with "but it's written" regarding scientific progress. It were only the christians whose reaction to people like Galileo or Darwin was similar as if the scientists would have proposed eating children. (Though judaism + islam have different no-go-areas...)
Science disproved a lot of details that the christian churches insisted on being right. But times have changed and so have the christian churches (well, most of them). In 2000 even the catholic church admitted that burning Giordano Bruno might have been a mistake... People will believe or they won't regardless what science says. If someone believes in a flat earth or creationism you can show them a thousand cast iron proofs and it won't change a thing.
So, to answer your question: nothing would happen. People would have to develop their own morale, their own ethics instead of following preset values.
In my opinion important is -no matter whether you believe in a god or not - that you believe in yourself.
Science in fact has already disproven religion in many aspects already. We can see the impacts on society as whole due to this, just looking at the number of people around you who decide to be atheists and not follow any religion. It is somewhat like how it was back in the great awakening (if I listened enough in history) however in this case it’s due to people looking more at reality than trying to hold a belief. Honestly nothing major would happen, but radical ideologies would likely fade a way quicker (good thing). This would result in more equality within one another, but there will always be those who still believe in a religion and won’t be fazed by any of this. So overall I’m pretty sure more people would start calling themselves atheists which has its benefits to society, but there will always be those who keep believing in it.
Well, science is on this already. Some scientist doesn't believe in higher powers, but I believe is a personal thing. I have my conviction in what I believe irrespective of what science says. Believing in God is optional