Deploy a set of EC2 instances, install MongoDB Community Edition on them, and establish a database. Set up continuous synchronous replication from this new database to the on-premises MongoDB database.

Set up an AWS Database Migration Service (AWS DMS) replication instance, configure a source endpoint for the on-premises MongoDB database using change data capture (CDC), and define a target endpoint for the Amazon DocumentDB database. Then, create and execute a DMS migration task.

Develop a data migration pipeline using AWS Data Pipeline, specifying data nodes for both the on-premises MongoDB database and the Amazon DocumentDB database. Schedule a task to activate this data pipeline periodically.

Utilize AWS Glue crawlers to create a source endpoint for the on-premises MongoDB database and set up continuous asynchronous replication between the MongoDB database and the Amazon DocumentDB database.