YITH WooCommerce Ajax Search allows users to search products in your shoping website. It shows the search results in real time.
I will recommend you buy this plugin from YITH official website which is here https://yithemes.com/themes/plugins/yith-woocommerce-ajax-search/ But if you are planning to start your shop with a limited amount of money then you can buy from here. Once you hit success, you can get the licence key from them and thus you will get future updates and support from them.
The search bar is the most common and important tool for any type of website but it’s often not performing enough, it only shows a limited amount of products and it’s slow and hard to use.