Architecture of a product search engine

I have developed a product search engine using AWS API Gateway, Lambda, ElasticSerach services. When user queries for a product, web server forward those request to API GW, then Lambda function is called and Lambda runs a search query in ES and sends back the results.

This works fine but I want query results to be cached somewhere if it returns more than 40 items so users can move to next page and so on without triggering the Lambda again and agin.

Is there an easy way of doing this without creating a web service using Node.js or something like that, I was checking ElastiCache but I couldn't find a proper use case.

Any idea how this can be achieved without maintaining a 24/7 web service?

Thanks!