There is no active timer in the game other than hunger eating away your characters slowly. (in most game modes you have plenty of resources to deal with this, including an infinite source of food in some instances)
Game time only advances when you sleep in a bed. This is always a choice the player makes. You can finish the game without sleeping once, although you do miss on things if you do so,,. But no time trials.
I recommend trying out the demo. It gives a pretty good idea on what to expect.