I did it for my TL, but I don't know that it's realistic.
In South America there is a surviving Gran Colombia (wrought with internal strife and intermittent rebellions in Venezuala, but managing to plug along), with a large PoD and explanation but the short one is Bolivar dies in 1829 and Santander succeeds him.
In the U.S. they have an earlier Civil War instigated by Zackary Taylor who dies a bit later, but still very early in his term (right around the start). The result is a more competent Confederate rebellion. The U.S. sinks a few British navy ships hauling supplies into Confederate ports, touching off a crisis which ends with European support for the U.S. and a Confederate "victory". The border's at the 36° parallel except the Virginia border and Missouri dip, while the Confeds also end up with a small strip of southern New Mexico, Arizona and Southern California. Between 1856-1874 there's some residual angst from the U.S. towards the Confederacy, but after a couple bloody border skirmishes the U.S. government takes the position of not recognizing the separation, but dealing with the fact they are separated.
Mexico ends up with a more successful Ferdinand regime, but not before Santa Anna sold a bit more land to the Confederates (a slightly lower border and Baja I should mention, which was originally purchased at the end of the Mexican-American War which happens as in otl). The 1860s are full of American intercontinental railway development, which eventually pressures an Atlanta-Austin line in the CSA. With a more successful Ferdinand regime the Mexican railway finishes in the early 1870s from Mexico City to Veracruz at continually gets expanded thereafter. In the late 1870s, an aging Ferdinand instigates railway lines being built up north to help populate the region, which ends up being a complete waste of time and money but lays down tracks close enough to the Confederate border in the future a Confederate-Mexican link would be possible.
Meanwhile in all this time Gran Colombia manages to get a national railway. The Panama Line would have been running for some time, and Mexican expansionism connects both lines in 1874, meaning Mexico > Central America > Gran Colombia. By the late 1880s/early 1890s the United States connects a line ending in Washington D.C. with a branch in Richmond, connecting the continent for the first time. Soon after the Mexican government and Confederates reach a border crossing agreement at Laredo, which becomes the junction for both railways. At this point, a person could leave New York and travel only by rail to the Peruvian border. I wrote down that Gran Colombia-Peruvian detente lead to a rail-connect across the Andes (there was a Transandean Rail of sorts iotl), which with a small carriage south of that border could lead to Chile. Thereafter, a rail could be taken to the Argentine border, and from there it's just a long train to Buenos Aires.
By the early 1900s I imagine many of these railroads could be better linked, but it's going to inevitably end up disrupted in the 1920s-1940s. Hardly perfect and I had to skip all the other intrigues, but it would be more than possible in the context of my TL.