There were several 'great treks' in our own time-line and the largest was the one made by the Mormons in order to set up their own state of Deseret. Some of them came all the way from Central Europe, thousands from London and the industrial heartland of the Empire, tens of thousands more came from the Eastern USA where they were being oppressed. More than half of them made the journey using hand carts rather than ox carts. A few years later the USA expanded westward and destroyed their dreams, taking their land and corrupting their religion.
There were also the almost continous migrations of the native peoples starting in the British colonies in the 1700s and ending with the USA in control of the whole of what is now the continental USA in 1910. Again, they treked but the USA followed.
If you want an alternative time-line where a trek works you need some sort of way of stopping the dominant power US, Britain, France, Spain whoever following or at leat not following until the trekers can defend themselves.