Before the final race, in the scene where Red Pollard (Toby McGuire) is riding in the yellow convertible with Mr. Howard (Jeff Bridges), Red is trying to convince Mr. Howard to let him ride Seabiscuit, in spite of his serious leg injury.
As Mr. Howard is pondering the request, he turns on the car radio, which immediately begins to play.
"Seabiscuit" is set in the 1930's. Any car radio made before about 1960-63 was a tube-type, and took many seconds to "warm up" before you could hear anything. "Instant on" radios were made possible by transistors, not discovered until 1947, and not used widely until the 1960's. (I learned to drive in a 1958 Ford, which had a tube-type AM radio--took forever to warm up!)