Brown Micarta was likely introduced in the early months of 1959 or perhaps even earlier. The image below shows pages 14 and 15 from the 1959 Randall Made Knives catalog dated February 18, 1959.  On page 15 there is a reference to Brown Micarta being an optional handle material on Models 1, 2, 3, 4, 5, 7, 11 and 12 (6"). 

I recently discovered that some of the first Randall Knives with Brown Micarta handles were pinned in the first week or two of production because of uncertainty at that time about the new handle material and the pitch, resin, or epoxy being able to "hold up".  Photos of three such knives that are known to exist are below. 

1959 Pinned Brown Micarta Model 1-8 & 2-8 (Pinned During First Week or Two of Production)