Actually, the first Hecate, at a minimum, had to appear in 2353, a decade and a half earlier. This is, of course, assuming the Goliath was an Orion (pretty reasonable idea, of course).
Given that it is a Terran ship, and most of the Terran shipyards were in Sol when the Orions were built, there probably weren't too many shipyards outside of Sol capable of building a Hecate. Even 32 years later, with the Colossus being built and the divided Terran territories, there probably were only a few initially built, and only recently were new ones being constructed to replace the loses incurred during the NTF rebellion.