This is time-based. You have to escape 20 times to get this. Since getting out is a race, you need to be able to traverse the entire course in under around 8 minutes.
The maze is randomized. However, you do not need to be #1 after the hospital. I'm always #2 and I still escape.
The key is to learn the way the maze works. Follow the red wires for the first two floors, then avoid any biomass in the sewers. Once in the sewers, the exit will always be near the steam pipes, although you may have to go up the small staircase. Look for the Exit signs.
Best of luck!