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If doing the mechanics with just two cards can be admitted as a form of side steal, Adrian Plate's excelsior change in Roterberg's New Era Card Tricks (1897, p. 22) is an ancestor.
A closer precursor to the Leipzig sleight appears in Mahatma, Vol. V, No. II, August 1901, p. 495. This is by Hal Merton (stage name of Walter G. Peterkin) and was published eight years prior to Downs's and Hilliard's The Art Magic, where the first description of the side steal is said to occur (See “Card Tricks Based on a New and Original System of Locating a Chosen Card: First Method”. Merton uses his left thumb to push over the top card of the lower packet as the right hand moves to replace the upper packet. This delivers the card into position to be palmed, identically to the standard side-steal handling.
Reinhard Müller notes that this method of palming a card from the center appears is described by F. W. Conradi in Der Moderne Kartenkünstler, 1896, p. 13. Conradi claimed the sleight as original with him.