We report the discovery of additional hot and massive stars in the cluster surrounding the soft gamma repeater SGR 1806-20, based on United Kingdom Infrared Telescope and Keck near-infrared spectroscopy. Of the newly identified stars, three are Wolf-Rayet stars of types WC8, WN6, and WN7, and a fourth star is an OB supergiant. These three stars, along with four previously discovered, imply a cluster age of ∼3.0-4.5 Myr, on the basis of the presence of WC stars and the absence of red supergiants. Assuming coevality, this age suggests that the progenitor of SGR 1806-20 had an initial mass greater than ∼50 M☉. This is consistent with the suggestion that SGRs are postsupernova end states of massive progenitors and may suggest that only massive stars evolve into magnetars that produce SGRs. It also suggests that very massive stars can evolve into neutron stars, not just black holes, as recently predicted by theory. The cluster age also provides constraints on the very high mass object LBV 1806-20.