Railways (including steam-driven railways) actually pre-date the Victorian era by many years.
Horse-drawn (or slave-drawn) wooden railways date back to Ancient Greece and were quite common in medieval Europe. A wooden railway built in 1515 at the Hohensalzburg Castle in Austria still exists and is probably the oldest railway still to operate.
The first steam engine locomotive was patented by James Watt in 1794. In 1804, Richard Trevithick demonstrated the first locomotive-hauled train in Merthyr Tydfil, United Kingdom. It was not successful though, as it broke many of the brittle cast-iron plates.
In 1811, John Blenkinsop designed the first successful and practical railway — a rack railway worked by a steam locomotive between Middleton Colliery and Leeds.
In 1830, the first intercity railway, the Liverpool and Manchester Railway, opened. The same year the first inter-city railway in America was opened, from Baltimore to Ellicott City, and this line was extended to Washington DC by 1835.
Hence by the time Victoria was crowned in 1837 railways were already numerous and successful throughout Britain and the USA.