Very recent observations of the $^6$Li isotope in halo stars reveal a $^6$Li plateau about 1000 times above the predicted BBN abundance. We calculate the evolution of $^6$Li versus redshift generated from an initial burst of cosmological cosmic rays (CCRs) up to the formation of the Galaxy. We show that a pregalactic production of the $^6$Li isotope can account for the $^6$Li plateau observed in metal poor halo stars without additional over-production of $^7$Li. The derived properties of the CCRs could then be used to put constraints on the physics and history of the objects, such as Pop III stars, possibly responsible for these early cosmic rays. Consequently, we consider the evolution of $^6$Li in the Galaxy. Since $^6$Li is also produced by Galactic cosmic ray nucleosynthesis, we argue that $^6$Li can be depleted in halo stars with metallicities between [Fe/H]=−2 and −1.