What's the fastest way to move a 2TB Oracle Database to EC2?

You can follow the strategies listed out in this document

https://docs.aws.amazon.com/prescriptive-guidance/latest/migration-oracle-database/migration-oracle-database.pdf

This document has a table that lists different utilities/methods that can be employed while doing a migration. Your choices can be different if you are moving to a EC2 based instance vs RDS Oracle. Depending on whether they have license for Data Guard or Active guard and/or Goldengate, how much downtime a customer can afford, network bandwidth, it becomes more of an art by selecting and recommending the right options. Generally speaking, Oracle native tooling is preferred over DMS if you are doing a homogeneous migration (Oracle to Oracle).