There probably is no definitive answer to this. It definitely wasn't Caldwell, though

It was probably no later than the 70's or so when the ability to record video media became more accessible to the general public- and even at that, who's to say there weren't some people who worked in the animation studios who had some fun putting some of the footage they worked on to music. There are vids listed (and in some cases linked) from back in the 80's. Probably the earliest well-known AMV would be the DaiCon opening animation...