Well, do Mercenaries count? They were payed to fight even though they did not really belong to a country. If Mercenaries count then this goes back quite a long ways, Nubia payed the Israelites and Pheneocians to resist Assyrian expansions and the Nubians were in turn payed by Carthage to fight against Roman expansion hundreds of years later. I believe that the earliest and best documented use of contracts were indeed used in Rome, Egypt and India used them to. But these were hit and miss, the elite of the military and most physically abled. In the Roman Republic a majority of the Army was indeed conscripted but the Centurions, the elite of the elite, were life long soldiers who might have started as conscripts but had survived, and worked their way through the Roman rank structure to become underpayed but highly respected soldiers.
Please note that 98% of what I say is my opinion and/or my "version" of the facts. Most of what I say is rumor with little to no evidence to back it up, just something I picked up somewhere.