When Cortez arrived in Mexico in A. D. 1519, he observed the inhabitants playing a ceremonial game with a rubber ball. The pre-Columbian inhabitants of Mexico began to use rubber around A. D. 1000. Thus, we can be sure that the game must have originated sometime between approximately A. D. 1000 and Cortez' arrival.
The conclusion reached above depends on the assumption that the game had been played since its inception with a rubber ball.