The Rogue One companion novel, "Catalyst", clarifies this. These days, those new books are full-fledged canon rather than "expanded universe" material. The Re

The Rogue One companion novel, "Catalyst", clarifies this. These days, those new books are full-fledged canon rather than "expanded universe" material. The Republic obtained those Death Star plans from the Separatists after the Battle of Genonosis (i.e. Episode II). The Republic started building it during the Clone Wars, they hadn't even been rechristened as "The Empire" yet.