1826, from everglade (1823), from ever, apparently in sense of "endless" + glade. Charles Vignoles's "Observations upon the Floridas" (1823) has Eternal Glades and Ever Glade morass.
The distance from the mouth of Hilsborough river to the head of the lake, in a direct line, is about 110 statute miles. The country between them is mostly, if not wholly, an everglade, by which is meant a low marsh frequently covered with water, and in which there grows a sharp triangular grass, from ten to twelve feet high, and impervious to men or animals. [American Mechanics' Magazine, Jan. 21, 1826]