It looks like they have been shooting for about a month...
Keep in mind i would say most movies take about a month to shoot-not big action movies but the same principal. By the middle of January probabbly at least half of its done. A lot of action movies go for around 100 day shoots these days.
I am also going to guess most of the movie isn't going to have any Digital special effects(or at at least a good bit of it. ) Scenes in offices, outside etc.. Which can often be most of the movie. You will be suprised sometime how little Digital effects are in superhero movies
There could be a decent chunk maybe a scene or two, i am going to guess in costume, possibly like a fight or something.
Or they could leave it out. Either way i could see it.
Castor
PS Curious if they have anything from Gotham in it