The fictional date.

Beale's expedition to survey and build a new wagon road at about the 35th parallel north was in 1857.

The route went from Fort Smith, Arkansas to Fort Defiance in northern Arizona and west to Beale Spring in northern Arizona and west to the Colorado River at Beale's Crossing north of Needles, Arizona, and west into California.

US Route 66 and Interstate 40 mostly follow Beale's Wagon Road.

25 US army camels were used on Beale's expedition, about 5 times as many as were shown in the movie.

So if Southwest Passage happened in real life it would be dated to 1857.

But since Southwest Passage is fictional its fictional date could be different. Most western movies happen between about 1865 and 1900, but there is no rule about that and I know of a few westerns set before the US civil War of 1861 to 1865.

In real history the USA acquired the lands in New Mexico and Arizona that the Beale Wagon Road passed through in the Mexican-American War of 1846-48.

Naturally once there was a transcontinental railroad most people going west would head for the nearest station on that railroad and take it west and then travel north or south from the station where they got off to their destination.

In real history the Central Pacific railroad road building east from California and the Union Pacific Railway building west from Nebraska met at Promontory, Utah and drove the symbolic golden spike on May 10, 1869. And if Southwest Passage happens in the same fictional universe as other westerns - like Union Pacific (1939) - that give the date of the completion of the transcontinental railroad, Southwest Passage should happen before 1869.

If Southwest Passage happens in the same fiction universe as other movies and television episodes featuring the US Camel Corps it might happen at about the same fictional date(s).