Search on default store

So I have a website and added the default store, configured it, etc. It lets me add some decent filters and custom categories. The one thing I am missing is a search bar so customer can quickly search for the specific item code and have it automatically filter down the store/inventory page to that.
So far the options are either to take you to a site search page or to create a custom shop. Is there no way to build in a search bar to the default store? (I don’t want to have to have to code in all the stuff like infinite scrolls, how it looks, etc into a custom store plus its harder to edit in the future). Thanks!

Link of the custom shop with search: .com/watch?v=8IcFmfti9P4
My site:
https://sebasmiles9.wixsite .com/misteremerald/inventory?sort=newest&page=2