Where would the construction of the Death Star need to take place due to launch requirements?

Entirely in space, likely at a Lagrange point or in a high orbit

The sheer quantity of material required to be lifted from Earth—potentially billions of tons—means that relying on terrestrial launch facilities would cause immediate collapse of global infrastructure, and the energy expenditure fighting Earth's gravity well is prohibitive. Therefore, construction must be moved off-world entirely. Orbital construction yards capable of handling kilometer-sized modules would need to be established in space, likely situated at stable gravitational locations such as Lagrange points or in high orbital paths. This setting minimizes the energy overhead per launch while allowing for the required massive scale of orbital manufacturing and assembly operations.