the rush referring to the traffic rush at the end of a business day when everyone is leaving work at the same exact time and they croud the highway so the phrase beat the rush means going to your destination before the highways are rushed and crowded by cars

To “beat the rush” means to arrive at a place or travel on a route before a large group of people also arrive or travel in that place. For example, if a restaurant gets very busy at 6 o’clock, you would want to get there at 5:30 so you could “beat the rush”. Or if traffic is very bad at 5 o’clock, you could leave at 4 to beat the rush.

it could mean to win some kind of race