1680s (trans.), "to shake to and fro" (especially of money in a cap, as part of a game called hustle-cap), metathesized from Dutch hutselen, husseln "to shake, to toss," frequentative of hutsen, variant of hotsen "to shake." "The stems hot-, hut- appear in a number of formations in both High and Low German dialects, all implying a shaking movement" [OED]. Related: Hustled; hustling. Meaning "push roughly, shove" first recorded 1751. Intransitive sense "bustle, work busily, move quickly" is from 1821.
The key-note and countersign of life in these cities [of the U.S. West] is the word "hustle." We have caught it in the East. but we use it humorously, just as we once used the Southern word "skedaddle," but out West the word hustle is not only a serious term, it is the most serious in the language. [Julian Ralph, "Our Great West," N.Y., 1893]
Sense of "to get in a quick, illegal manner" is 1840 in American English; that of "to sell goods aggressively" is 1887.