The Roman Catholic Church has the start date as 1091. Historical sources in English are a bit sketchy but this one seemed to agree with most.....
> ....[T]he custom of distributing the ashes to all the faithful...is mentioned as of general observance for both clerics and faithful in the Synod of Beneventum, 1091 (Mansi, XX, 739), but nearly a hundred years earlier than this the Anglo-Saxon homilist Ælfric assumes that it applies to all classes of men.
Makes the 10th century seem a good time frame.