If we assume that the Gaiden took place in the middle of the war, that Minato became Hokage after the war (reasonable, since he probably acquired his fame thanks to the war), that Minato and Kushina "celebrated" the night that Minato became Hokage and Naruto was born 10 months later, then it's most likely more than a year...
It was more than a year and Obito already proved to be more gifted in controlling his Sharingan than Sasuke (still Sasuke supposedly possessed the strongest eyes since Madara and later did in fact obtain EMS... at least Kyubi considered his spiritual powers comparable with Madara's and Tobi/Oro mentioned that his eyes are going to be stronger than Itachi's), simply by immediately activating it in a proper (2 megetamas in each eye) version, indifference to Sasuke.
What's more, it's like this in Narutoverse: weak people (sick etc.) --> normal people --> ninjas --> gifted ninjas --> genius ninjas --> Uchiha --> Uchiha Geniuses. Even if he wasn't as good as an average Uchiha (which already surpasses genius ninja like Oro, simply thanks to the things that Sharingan with their blood allows), after awakening his Sharingan it isn't impossible, heck it isn't even anything special when you look at Uchiha Geniuses like Shisui or Itachi.
Shisui looked quite young to me, probably younger than Kakashi (which would mean we has younger than Obito as well), but it's hard to compare his age, a few days before the Massacre with Kakashi's, since we haven't seen Kakashi at that time, that age. There is even an interesting fanart that shows the age difference between Obito, Shisui and Itachi:
Shisui's age is still vague, yet it is quite possible that he was younger than Obito and if that is true, then think what he did at the same war in which Oibto was participating to some point. Shisui, the kid standing beside Obito (in that fanart ), at the 3rd Ninja War, became to be known as Shisui of the Body Flicker, the strongest Genjutsu user of the Uchiha. At that time, it's quite possible he already had his MS, considering that when Danzou used Shisui's MS, the Mist Byakugan user noticed the same kind of chakra that Shisuis used and supposedly the difference between Chakras when using a normal Sharingan and MS is quite big (too big for the Byakugan user to not notice).
The MS, is really a special tool, not to mention the ones belonging to Shisui and Obito, those two pair of eyes seem to have the most special abilities in their respective categories of one-eyed jutsu. Seeing how famous, how much feared and how powerful was Shisui at that age with MS, is it really so hard to imagine Obito a few years later, after obtaining and training his MS, being as formidable as well ? Not to mention that it is confirmed that Tobi is boosted with Hashirama Cells and it is already proven just how much of an influence they have on MS.