It’s essential to provide access to the search box on every page because if your users cannot find the content that they are looking for, they will try to look for it on other websites. More on how to create perfect search bar:
Design a Perfect Search Box
Search box is a combination of the input field and the submit button. One may think that the search box doesn't need a design; after all, it's just two simple elements. However, on content-heavy websites, the search box is often the most frequently used design element.
Check the examples: