I know that the first two slots aren't available yet, but I can't find third slot.

The Red Daddy Orc.

I've been looking everywhere on all three time settings (Day, Evening, Night). I think maybe I actually already got it but its bugged.

Does anyone know where I can get this card?

you'll have to visit the barracks in the afternoon (and you might have to increase your affinity with Beton to access the room)