If search is a primary function of your site display it prominently, as it can be the fastest route to discovery for users with high intent to convert.
Principles of Mobile Site Design
Nick Babich
39111

I might have a slight issue with this point, if we’re talking about a non-e-commerce mobile website, I don’t think users even use the search functionality of a website (largely because of how many websites have implemented it wrongly over the years that users don’t trust it). So, we could replace it with a live messaging tool like Intercom or Drift etc.