Connect Customer Databases directly to a Webapplication for uploads

I'm currently working on my bachelor in Business Information Technology. For my final work I need to evaluate a interface management for a cloud application. The users should be customers, which have their own databases. Now if they want to upload some Data from the database, I want to make it possible, that they don't need to make an export and upload it afterwards. They should can do a direct upload. And everytime they logout and login, the connection should be open again.

Now my question is if and how it is possible to link those databases directly to my application?

No code needed! - Just concepts..

I already thought of ODBC, but I am not really shure if it would work with it as a "ODBC Engine" between my application and the databases.