Science & religion are not mutually exclusive - unless you wish for it to be so.
All the major religions have a cosmology & within that an originary myth. And almost all mention a chaos & then an order imposed. Quite how that differs from the 'Big Bang' I'm not sure.
Most people look towards religion to give meaning, cohesion & continuity to their lives, and not for originary myths. When people claim their religion is the true religion they're not using the word 'true' in the same way a mathematician & physicist would use. Truth in the way a science uses it is simply not important to them, this is one reason why the mythology & rituals may be inconsistent with each other.
Religion is a complex & sophisticated attitude, for example:
Marcus Aurelius talked of atoms (he knew of Democritus work) - and so was a materialist; but he also talked of gods and God (not neccessarily the Christian one).
The Mughal Emperors & their court saw similarities between Islam & the Brahman of the Upanishads.
Of course this isn't to say that it can't be superficial, obscurantist, petty & corrupt. But this is as much true for all human activities including science: the petty bureacratisation & divisionalism of knowledge, superficial pop science & big science.
Although Science is claimed to be an objective representation of facts & theories of the world, and to some extent this is true - and this mainly when deeply studied ; but also it has an ethical, moral & religous outlook that needs to be examined. When one looks at one of the work of one of the very early materialists schools - epicureanism -as detailed in Lucretious poem de rerum natura, one is struck by how much the work is also about human life in all its ramifications - Lucretious understood materialism affects not only your view of the non-human world, but also of the human world of social relations, ethics, & religion as traditionally concieved.