Assuming your talking about the top line players making millions, because your median professional athlete is barely covering there costs if you include athletes outside of the big 5 sports in the US and those outside of the top flight leagues. Then like any performer embedded in the monoculture it happened when mass media became a thing.

Once your able to sell discs, tapes, TV ads on a mass scale with extremely low marginal cost anyone with a claim to that media property can make millions off of it.