Of course the parents have a role, and usually the larger role in the upbringing of any child of theirs, but it is a general fact that most people do get their religions from their parents (having such) and/or the culture and/or any education likely in the country in which they live. And being so - what the parents impart to the child - is reasonably not up to the child to decide, hence it is more indoctrination even if you might call it education, given that such will vary depending upon where one is born. In this respect - as to believing in God or not - it really is mostly up to the parents' beliefs - until a child is old enough to start questioning, that is. And many never do so. No child is born with any such belief - not in my view anyway - even if they might project their thoughts on to what they see about them, just as they might do with the animals or dolls in their life - giving them some special existence.
I am rather grateful to my parents, especially my mother who was probably the most religious of the two, since she didn't try to force anything as to religion upon me or my brothers. Her example as a decent human being was rather sufficient in my view, and I could hardly fault her bringing us up.