Here is AWS support answer to this question:
I would like to inform you that you can Amazon Cloudwatch logs to log
user activity on your application, you can refer to the following
documentation for the same.
[+]
https://docs.aws.amazon.com/AmazonCloudWatch/latest/logs/WhatIsCloudWatchLogs.html
CloudWatch Logs enables you to centralize the logs from all of your
systems, applications, and AWS services that you use, in a single,
highly scalable service. You can then easily view them, search them
for specific error codes or patterns, filter them based on specific
fields, or archive them securely for future analysis. CloudWatch Logs
enables you to see all of your logs, regardless of their source, as a
single and consistent flow of events ordered by time, and you can
query them and sort them based on other dimensions, group them by
specific fields, create custom computations with a powerful query
language, and visualize log data in dashboards.
You can also consider using Amazon Timestream to store and analyze
events on your application. You can then ingest this data in
Quicksight to visualize and build dashboard.
[+]
https://docs.aws.amazon.com/timestream/latest/developerguide/what-is-timestream.html#what-is.use-cases
Amazon TimeStream is a fast, scalable, and serverless time series
database service for IoT and operational applications that makes it
easy to store and analyze trillions of events per day up to 1,000
times faster and at as little as 1/10th the cost of relational
databases.