Marley was like 10 or 12 when people started playing ska... Nobody in particular invented it, it just sort of came about.

Short history lesson:

Lower-class black Jamaicans have entertained themselves with outdoor music parties since they were enslaved and taken from Africa to the Carribean. For most of history, they had live bands. Economic and social realities in the 1940's made musicians hard to come by, so people started playing records on old record players hooked up to PA systems (these were actually the original raves in a way). American R&B, and a little jazz, was what they played. These 'sound systems' got bigger and bigger, and began competing with each other for customers. The primary way they competed was by playing new and/or exclusive records, normally obscure R&B tunes, that other systems didn't have. By the mid-1950's the big operators (first Coxsone Dodd and Duke Reid, a little later Prince Buster) realized that recording their own songs would be a great way to ensure exclusivity.

At first, it was all just straight R&B, but musicians and singers innovated by incorporating rhythms and sounds from the local calypso and mento music (as well as bringing Rastafari drummers and their flat-out African beats into the studios). By 1958 or 1959, it was ska. Most of the music that we listen to from 1950's and early 60's Jamaica is ska, but there was still tons of straight R&B being produced - if you can track down the Wailers album "One Love at Studio One (1964-1966)" (i forget whether i found it on torrentspy or thepiratebay, should still be active though), you'll get a kick out of hearing Bob Marley singing stuff like 'teenager in love.'

Also: the musicians later known as the Skatelites were the main studio band throughout this time, playing for just about every singer in the country. They were extremely talented and serious musicians, hence they loved jazz. that's why ska horns are they way they are.