I didn’t try it myself yet, but can’t you do cargo at night when the mission has real-life weather (red dot on it) and it’s night-time in this area IRL?
I’m pretty sure i’ve seen a streamer flying these missions at night.
Live mode does work in some way, but very limited.
If you move the time slider, you will see some red dots appearing on some of the missions on the map.
These missions will have their start time adjusted to the slider position and can be flown with historical live weather (you can check there will be historical METAR data for the airport in the EFB).
But I never see any of the red dots for night time.