To build the shelter, there is a problem that Perfikot must solve, which is the shield machine.
Although the shield machine may not be impossible for the engineers and alchemists of this era to build if the requirements are known, clearly, in an era where even the swinging arm drill hasn't been invented yet, making a shield machine that meets Perfikot's requirements is quite difficult for these people.
In Perfikot's original world, the most primitive shield machine was indeed invented during the same era, but rather than being a shield machine, it was more of a construction method.