If the user can access the Sharepoint site, you can just link to download link of the document on the Sharepoint site?
If the user cannot acces the Sharepoint site, you could stream it yourself, but that's hardly recommended.
Why can't you just link to the download link of the document?
EDIT:
You specifically want to know how to make sure the link opens directly.
For this you need to change the MIME type of the Response (the download) to provide more info to the browser how it can open that link.
More info in this answer: https://stackoverflow.com/a/2806749/65087
In my applications, I generally create a Util method that can provide a MIME type, based on the extension.
This solution will work if you can offer the download yourself for your Controller, eg. by calling the File() ActionResult.
This also requires you to have access to the physical file, so you can stream it.
So, I'm not sure this fully answers your question, since you said the document is on a Sharepoint site...?