Cricket in the Early Days

In the early days, did british colonists encourage native populations to join in with them in playing cricket? Or was it principally seen as a white man's sport? Most of them tried to just imitate the british they saw them playing on the field. They would just try makeshift bats, a ball made of something else other than leather. And more than its practical impact on native societies, cricket served a very significant ideological function in making the natives closer to european civilization. Playing cricket was the quintessential british game.