The Seattle-to-Los Angeles train struck the Ford Focus on Wednesday near Guadalupe, about 10 miles west of Santa Maria along California's central coast.
The engineer told investigators he saw the car and sounded the horn, but the driver backed onto the tracks and stopped moments before impact, the San Luis Obispo County Tribune reported.
There is only a stop sign at the dirt road crossing.
The 25-year-old driver was hurled into the lettuce field and died on impact. The little girl died later at a Santa Maria hospital.
Authorities haven't released any names, but Gabriel Vasquez identified the driver as his cousin, Antonio Garcia Ortiz, the newspaper said.
Vasquez said his cousin got a call from his baby sitter saying he needed to pick up his child because she had a family emergency. Ortiz then returned with the infant to the field to get his wife.
Vasquez said field workers sometimes forget about trains on the track.
Vasquez said he believes it was a tragic accident, and Ortiz wouldn't deliberately hurt himself or his daughter.
There were no injuries to the 132 passengers and crew aboard the train, which was delayed about four hours, Amtrak spokeswoman Christina Leeds said.
Information from: The Tribune, http://www.sanluisobispo.com