PCB design often (always, actually) occurs post circuit design, mainly because it is difficult if not impossible to layout component pads and connections without knowing what the components ARE and HOW they are connected, Some of us are good at circuit design, and some of us are good at turning circuit designs into PCB designs, Some of us do BOTH as a hobby activity, but if you are seeking employment it makes sense that you concentrate on the job you would be asked to perform. You have been given an "impossible" task, so I would not waste anymore time trying to convince this particular employer that you are qualified to perform PCB design.
If you are really seeking employment, you need to define what tasks you believe you are capable of performing. This includes recognizing impossible requests. You never want to work for someone who issues impossible (or ill-defined) problems and then expects you to perform. Find a potential employer who is responsive to your capabilities. If applying for a PCB design job, bring some examples of your work to the interview and provide the information to the potential employer of what software you use for PCB design. They may already have PCB design software that you are expected to use, but do not miss this is an opportunity to find out what you "need to know" to qualify for the job.
I apologize for responding to an older (dead) post.