This depends very much on the person writing. Generally, atheists do not capitalise the word ‘god’.
Theists – those who believe in the existence of a god, such as Christians, Jews, and Bahá’ís – generally capitalise the word ‘god’ when referring specifically to that god – because to them that is not just a god, it is the god – the one and only god that exists. (And even if that god is thought to have a name, the word ‘god’ itself is often used in place of that name – it refers to a single, specific being.)
Atheists sometimes do and sometimes don’t capitalise the word ‘god’. Those who do often do so because that has been the convention in writing for hundreds of years, and it makes it clear that they are specifically referring to the Christian god or the god of another monotheistic religion. Many atheists do not capitalise the word ‘god’ because they do not think that a god exists, thus there is no single, special ‘god’ that they are referring to.
In any case, it is best to be consistent in when and why you capitalise the word ‘god’ throughout any piece of writing.