You get missions all the time now even in the first few days, some are easy some are tough.
I just got a mission that i had to babysit 2 people for 5 days and keep their happiness above 20%, you control them during that time (easy right?) so the game decided to throw a plague at me that ended up killing the 2 visitors and infecting 5 out of 7 of my colonists (2 died).
I also got raided in the meantime. Fun fun!