I have no idea if whistles were used from the start, but I actually once called a game without using a whistle! It was many, many years ago when I had first joined our local kids' rec league Board of Directors. We would make sure there was a Board member at every game. I was assigned a 3rd grade boys game to watch and eval the refs. However, there was a scheduling problem and neither one of them showed up.
I really had no other viable option other than calling the game myself. I had on a blue T-shirt with jeans and, fortunately, tennis shoes. I spoke with both coaches and we agreed that I would raise my hand and yell "STOP" in lieu of the whistle. I pretty much stayed around mid-court which turned out to be fine since it was a small elementary school gym court.
Actually, it worked out somewhat OK. I figured the boys were used to an adult yelling "STOP" at them.
From that point on, I always took a whistle with me to those assigned Board games - and I kept a spare jersey in my car. However, I never had to work a game like that again. But better safe than sorry.