Of course science cannot prove that there is no god.
However, the basic difference between scientific theories and religious or faith beliefs, is that in science, a theory is offered, and people try and find counter-examples, or ways in which the theory is weak, fallible, or incomplete. Much of the business of being a scientist is testing theories, critically, and trying to improve on them, or disprove them.
In contrast, in all the major religions, the believer is supposed to accept what's taught, not challenge. It's an opposite way of thinking about the world.
In my opinion, there are many scientific discoveries in the last few centuries which strongly suggest, to me, that the bible and other religious books were wrong and highly fallible. To the extent that they cannot be trusted, at all, as a basis for any sort of belief, given what we now know about the world in general.
And, especially for me, a knowledge of linguistics and translation, and the difficulties, or impossibility, of accurately understanding the exact detail of a text written in a different language in a different time in a different culture, makes it impossible, for me, to be able to take anything in the bible as necessarily correct or valid.
(my phd was primarily about translation and understanding across languages and cultures, and comparative linguistics, so this issue is very important for me).
That is why many atheists say that yes there is a huge difference in a religious belief or a scientific belief. Even though some scientists, or atheists, can seem to be "just" being as dogmatic in their own way as people with a strong religious belief. The scientific, rational, atheist position is looking at what evidence and knowledge we do have, in the current world, not 2000 years ago, and using that to build a "best fit" hypothesis of how the world is. And if you do that, it's rather hard to also adhere to standard Christianity.