One third of the real cowboys were Mexican, another third were Black. Cowboy was a terrible job, and they were mostly despised as "saddle tramps' until the sheep herder/cattle rancher wars. The ranchers, and later Wild West shows, played up the romance of the cowboy.
I am a fluent English speaker (in the US for a few decades) who knows Spanish (native speaker of Portuguese which also uses vamos), and thinks about etymology all the time - it never occurred to me lol. I just thought it was some weird old timey american thing lol
1829, "move off or away, get out," American English slang, of unknown origin, perhaps related to British dialectal mose about "go around in a dull, stupid way." Or perhaps from some abbreviation of Spanish vamos (see vamoose). Related: Moseyed; moseying.
Funny thing related to this: I've heard that the Chevy Nova (car) was put out for sale in Mexico. No one bought it because "Nova" = "No va" = no go. No one wanted the "no go" car.