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Ishinan's comment: My source says otherwise (see below)
POUSSER : Prononc. et Orth.: [puse], (il) pousse
[pus]. Homon. pouce, poussa, poussah. . Étymol. et Hist. A. 1. Fin xives. «exercer une pression sur une chose
pour la déplacer» (Froissart, Chroniques, éd.
G. Raynaud, t.9, p.248). Froissart's Chronicle was written in French by
Jehan (Jean)Froissart. It covers the years 1322 until 1400 and describes
the lead up to and the progress of the first half of the Hundred Years'
War.
Here is the text where the first occurrence of "pousser" in
Middle French is found:
What is your source?
Ishinan