Write a better search algorithm to reduce load time on a php web app

I have a working sample on this website: [login to view URL] and this table is generated through wordpress woocommerce database filtering specific products with certain category and lists their attributes. The working sample loads up pretty fast but when we have over 3 thousands products the loading takes forever. You need be able to write a better solution (lots of coding involved) to retrieve data from database in a better way which saves time. Right now the table loads all the products but doesn't displays it but we need to make sure it only loads and display the data that has been filtered. probably righting some ajax and applying loading animation is the solution but then again the search module itself needs to be adjusted. so we have to balance the load and apply better algorithm. Please examine the site before sending proposals. Lots of coding and reading the present code involved. So you need to be an experienced wordpress programmer in order to do this task.