How to implement C# web application authentication without notifying user about authencation?

If you want access to the users account, they have to be involved and they have to give their credentials via Oauth, which means you do not get them.

Once they have authed that first time, you get a token you can save and use instead, and you can use that silently - but to get that token, the user must be willingly and knowingly involved.

Richard's correct, the user needs to be involved at least once to authorize the app to access their account. There's an OAuth guide that outlines this here:

https://www.dropbox.com/developers/reference/oauth-guide

The only exception is if you only intend to have your app connect to your own, single account. That is technically possible, though it generally isn't recommended.