Building a web analytics engine is a complex task that can be broken down into smaller components, each of which can be solved using existing open-source tools. By leveraging Snowplow for data collection, Athena as the main data warehouse, MySQL to store pre-aggregations, and Cube as the aggregation and querying engine, developers can create a robust analytics platform. The process begins with setting up the tracker on the website, followed by configuring the collector, stream enricher, S3 loader, and query engine. Once the data is collected and stored in S3, it can be queried using Athena or Presto. The Cube API is then used to build analytical applications, including the creation of a sample data schema for events. The frontend application is built with React, Material UI, and Recharts, allowing users to interact with the dashboard and view charts such as page views, sessions, and users. To add interactivity to the dashboard, developers can use date range pickers and implement filters to slice and filter the data. Finally, by using external pre-aggregations in Cube, developers can optimize performance and cost by reducing the number of queries executed against Athena and storing aggregated data in MySQL.