I specifically mean war started for religious reasons rather than war that change the religion of a place after a war.
This question has been discussed before on this subreddit.
The consensus - as far as I understand it is: yes, but you have to define what you mean by holy war. Pre-Judaism monotheism was a rare thing, most cultures had several gods or whole pantheon. So while people fought in the name of one or more gods, it often was to show that "my god is better". They abducted holy objects and declared gods of conquered people to be dead or defeated by the god / gods of the conqueror. To wage war as a way of spreading your belief, is more likely to happen in monotheism where there is "one true god" - although there are instances of polytheistic cultures who wage war with religious justification, see Assyria. And even here we have to consider purely political / economical reasons for war, with religion as a pretext. Human interaction is not as black and white as we who seek to understand it would like it to be.