[make] a break for

to attempt to escape quickly or suddenly from a situation or place

When they saw the opportunity, they decided to make a break for the nearby woods to avoid the pursuing enemy.
As soon as the door opened, the cat made a break for the garden.
When the teacher's back was turned, the students made a break for the classroom door.
As the alarm sounded, the thief made a break for the exit with the stolen goods.
When they saw the guards were distracted, they decided to make a break for freedom.