Hickman's Avengers and New Avengers has been building up to Secret Wars from their very beginnings, when he started writing them in 2012. Time Runs Out is just the final arc leading into Secret Wars. Nothing else is essential for Secret Wars as far as we know at the moment.
However, if you want to be caught up on the major changes in the status quos for characters like Captain America, Thor, and Iron Man, you may want to read their respective series as well as the major events like Original Sin and Axis that they tie into. I would probably recommend checking out
Marvel Unlimited for a cheap way to read all that.