I am able to connect to an Oracle database using the REST API, but I want to connect to it without the REST API. Is there any another way to connect to an Oracle database?
The short answer, No.
Oracle JET is a pure client-side toolkit. It does not run or process on the server. Because of that, the only interaction with data resources is via Web Services of some kind. REST is the most common. You could use WebSocket, or Server Sent Events as well, or some other method that a pure client could communicate with.