This change first appeared in French, in the Jan. 1905 issue of I'Illusionniste, Vol. 4 No. 37, p. 5, with a byline of Van Lamèche. Professor Hoffmann, in Later Magic, identified Van Lamèche as a Belgian magician, but there is reason to suggest that Van Lamèche (a probable pun: vend la mèche = reveal the secret) was a pseudonym of Jean Caroly, editor of L'Illusionniste, and that Van Lamèche or Caroly were performing the same function Ellis Stanyon did in his English journal of the same period, Magic: explaining tricks he had seen rather than invented.
The Snap Change didn't appear in English until three years later. W. H. Dilger published the move as “Change Cards by Snap of Finger” in The Sphinx, Vol. 6 No. 12, Feb. 1908, p. 144. Eight years later, H. Syril Dusenbery managed to get it into the pages of The Sphinx again, this time under the title “The Flip Change” in Vol. 16 No. 12, Feb. 1916, p. 232. He reports learning it from Theodore Bamberg, which probably occurred during an October 1914 meeting of the Pacific Coast Society of Magicians, where Dusenbery reports Bamberg performing the change (see The Sphinx, Vol. 13 No. 9, Nov. 1914, p. 169). Curiously, five years later Dunsenbery contributed the same sleight to Felsman's Magical Review, Vol. 2 No. 6, Nov. 1921 - Feb. 1922, p. 6. There he does not mention Bamberg and leaves the reader to assume the sleight is his (Dusenbery's) invention. The previous year Bamberg had published the sleight himself, in Quality Magic, 1921, p. 16.
Horace Goldin is frequently credited with this sleight due to the “The Goldin 'Visible' Change” appearing in Victor Farelli's Farelli's Card Magic, Part Two, 1933, p. 70.
There is evidence, though, to show that Stanley Collins invented this change before Bamberg and Goldin, and may have been the spring from which Van Lamèche and/or Dilger drew. Collins claims in his Gems of Personal Prestidigitation, 1952, p. 15 (not published until its inclusion in Edwin Dawes's Stanley Collins: Conjurer, Collectors, and Iconoclast, 2003), that he came up with the sleight in his early twenties–which would place it in the first decade of the 1900s–and he showed it around that time to Goldin, Harry Houdini and Chung Ling Soo. Further corroboration of Stanley's claim appears in The Wizard, Vol. 2 No. 17, Aug. 1948, p. 176, in a letter by R. C. Wilson; also see Victor Farelii's response in the Nov. 1948 issue, Vol. 2 No. 19, p. 247.