According to Aunt Wiki (and quite plausibly too) the word is derived from Greek λαπάρα [flank, abdomen] and τέμνω [cut, verb] / τομή [cut, subst.].
As according to the same source the first successful laparotomy was performed in 1809, one should infer that the word was coined and used - possibly only among colleagues - no earlier than that, as no surgeon in his right mind would taint his reputation by publishing a failure.
Merriam-Webster actually traces its first official use to 1878 (without providing a source).
OED mentions as a source “T. Bryant, Manual for Practice of Surgery”, publ. 1879.
70 years to transition from “better like this than dead” to “standard surgical practice”?