No story requires an actual villain but stories are normally about overcoming something and a villain fills the bill nicely.
That said, introduce the villain as soon as possible. Characters introduced late in the story tend to be ignored by readers because they are used to having all important characters introduced early on so as to become familiar with them.
But you don’t have to show your readers that your villain is evil. You can simply introduce him/her as a minor character and let that character become more important as the story progresses.