At what point of the design process the manufactures build their first prototype?
There is no definite answer that will fit all manufacturers and projects for the question you're asking. 

Simply put, the decision to create a scale model or a first prototype depends on what the goal of the creation is, the underlying technology, cost and market interest. A lot of aircraft, either new models or improved variants of already existing models never make it past the design stage. Other results in scale models to verify aspects of the underlying design or technology, while some may even skip this and go directly to a full-size prototype to be used for testing. 

In some cases, a manufacturer will build a prototype regardless of market interest, because it allows them to showcase the technology and show that it actually works, while other manufacturers might not continue to that stage unless they have generated actual orders for the aircraft. 

Needless to say these decisions will be based on different input from project to project, but generally speaking the end goal is to lower the risk if you decide to continue a project. If you are designing a very new aircraft, it makes sense to validate aspects of it before committing to production unless you can demonstrate that the risk is already low enough not to matter greatly.