Upload multiple files to SQL Server without access to the Server Box
If there are no transformations involved, you could write this process fairly simply in SSIS with a for loop in the control flow that iterates over a file directory, then passes each file name as a variable to a data flow.  The filename for the csv would be bound to that variable, and your destination could similarly be bound to the file name.  Just use bulk mode in your target component and you should get pretty good efficiency.  This works great if the folder is accessible to all users and you add a step to either check and see that files in the directory are processed or move them somewhere else when they've been processed.  The SSIS process could be invoked from the SSIS catalog on the SQL Server directly, or scheduled on a regular basis.

Alternatively, you could use the bcp Utility for a CLI experience.  This is probably a lot simpler in that it doesn't require writing an SSIS process and management of that process, but it requires more knowledge on the end of the user invoking it.  This tool doesn't require the files be on the server: you provide a path to the file as the invoking user, along with credentials to authenticate, and the tool will handle the data movement.