The "Underground Railroad" as a train/railroad had never really existed. That name describes a network of secret routes and safe houses during the 19th century across the Eastern Seaboard of the United States of America. The "railroad" helped enslaved African Americans escape to Northern states, and, after the Fugitive Slave Act, to Canada. The first literal subway/tube/underground railroad was built in London, England, in 1863, while America was embroiled in the Civil War to end slavery.
The series is set in the 1850s, but includes several deliberate anachronisms - subways, dynamite, typewriters, Oklahoma, etc. - to create the impression that it takes place in an alternate universe.