In the Alan Moore origin, you were supposed to pick up that he was referencing other muck monsters that appeared in the comics before Swampy, like the Heap (Hillman, 1942). Wikipedia gives his origin:
The original Heap was formerly Baron Eric von Emmelman (his last name also sometimes spelled Emmelmann), a World War I German flying ace who was shot down in 1918 over a Polish swamp. Clinging to the smallest shred of life through sheer force of will (and, as it was later revealed, with the mystic help of the goddess Ceres, later to be referred to more generically in the series as Mother Nature), through the decades his body decayed and intermingled with the vegetation around him, becoming one with the marshland itself until at last a shaggy, shambling half-world creature neither animal nor man arose from the muck during the early years of World War II, a creature which would become known far and wide as The Heap.
Resembling a huge humanoid haystack whose most visible facial feature was a dangling root-like snout, the mute monstrosity first battled the lupine-cowled Blackhawk-style Allied ace SkyWolf before turning against its fellow Germans who were now fanatical followers of the evil Nazi cause. Then it took to wandering the globe, helping in its semi-mindless and often misunderstood way those in need and battling those monsters more malevolent than itself.
Heap was probably based on Theodore Sturgeon's swamp creature "It," a short story published in 1940 (and later adapted by Marvel Comics). Solomon Grundy has a similar origin, but without the element of fire involved.