In Captain America: The Winter Soldier, how did S.H.I.E.L.D. know about Dr Strange?
It is mentioned in the scene on the rooftop that existence of Bruce Banner, and Steven Strange have changed the game.
So have to assume timing of movies should have in the movie universe (reversed in release of movies)
Dr Strange
Captain America Civil War
At what point S.H.I.E.L.D. learned about Dr. Strange?
We don't know precisely but we do know that SHIELD/HYDRA have been aware of Steven Strange since before Captain America: The Winter Soldier even if only as a potential problem/threat using Arnim Zola's algorithm.
Since they are aware of him it's logical that they were, at least, keeping him under some form of surveillance (or at least monitoring) so they would be aware of his emergence.
After all, that's what SHIELD now does, monitor and catalog gifted people....at least in the TV series and, by extension, in the MCU as a whole.
Equally, Thor is aware of Dr. Strange as we know from the post-credit scene in the Dr. Strange movie...so while that scene (we think) takes place after Civil War we know that the bulk of the movie takes place before it.
So, it's possible that Thor has kept SHIELD informed before he disappeared with Banner.
Before the events of (and during the beginning of) the film Doctor Strange, Dr. Steven Strange was an incredibly-skilled, highly-accomplished neurosurgeon. It is likely that this was enough to put him on SHIELD's radar.
