Since I liked the OP's question so much I'm going to try to help with the answer or provide some thoughts on how to get to the answer(s).
I think it's somewhat safe to say that in most businesses technology exists to support business objectives. So while sometimes pure R&D drives new products and services, generally someone starts with a business objective (such as increasing profit by decreasing costs and/or increasing revenues).
Once someone has done some high level analysis that indicates if some such product could be brought to market for X investment and produce enough Y profit over the life of the product to drive enough Z ROI to make the project worthwhile vs the other potential investments available to the company, then someone says, "well that sounds good financially but what are the parameters of this opportunity, ie: what are the '
market requirements?'"
At this point someone should have already gone to the marketing and sales teams to say "if we bring you this new product with these parameters, are you sure you can sell enough volume at the projected price in the forecasted timeframe? Because unless you can, there is no sense in the company spending NRE and other resources to even go down this path."
Once the sales, marketing, and other people are pretty sure that the new product with the key parameters will be successful, then the challenge is given to engineering (and sometimes other departments) to design something that can make it real with a high degree of specificity. At this point, somewhat early in the overall process, there is only a very high level specification, plus a preliminary budget and schedule. These documents are targets that are close enough to potential reality that it intrigues and motivates the business people but it's still somewhat vague for the engineering team.
After the market requirements are outlined by the business people ("it has to be this big or small, cost this much to manufacture so we can mark it up by this margin and still stay under this selling price, it has to provide these functions, consume this much power" or whatever), the market requirements then land on the desk of the engineering community who is tasked with turning the market requirements into the more detailed
product requirements.
The workflow can vary from company to company but at a high level it generally (but not always) goes from the business requirements to technical requirements. In big companies the process might be nearly overwhelmed with rigorous bureaucracy, in a smaller company the process might be much more informally driven by the instincts and power of personalities, but generally it starts with a set of business requirements that evolve into an engineering design.
I think for the purposes of helping the OP see the basic design process (and there are truly are many variations, so we're just talking "typical" if there is such a thing) it would be good to start at the point where the market requirements (including ISO or any other QA/QC requirements and any industry standard practices) have been largely established by management, the "product manager", etc. and the market requirements are now in the hands of engineering management. So in addition to the key parameters of the new product the market requirements document probably also highlights the key competitive products - so the engineering community probably has a rough idea of what the alternative designs look like, cost to manufacture, etc.
So, starting with "it's bigger than a breadbasket but smaller than an automobile, these are the "market requirements", so how do we design something that will give us the details of a good "product requirement" document that would be complete and clear enough that it would be sufficient for manufacturing to manufacture – and that will eventually meet the high level "market requirements" which will enable the sales department to be successful and the customers to be happy?"
For example, if the OP is working at a radio manufacturer and the market requirement says the objective is to design a radio that can be manufactured for $x of parts and labor and that supports the following the high level parameters -
what does engineering do from that point forward to design the product?
No doubt there will be some ongoing iterative discussions between the engineering team and the business team, but once the business team says here are the parameters of what we are trying to accomplish, and if the OP is assigned to design something that meets the parameters, what's the process from there? Or what are the top 10 things engineering is going to ask or try to solve as part of the process? These might be more process questions/suggestions, or they might be more technical questions/suggestions - but let's assume we know roughly what someone wants built and now we need to make the electricity work in circuits.
Net, net: I think it's good for new engineers to recognize that a lot of stuff happens upstream but in this case I think the OP is also trying to understand what happens after the business objectives have been largely determined. How do you design power supplies, analog and digital circuits, etc.? Do you start with inputs and work forward, or outputs and work backward, or some of both, or something else?
PS, ElbowPics, this is just my guess at interpreting your question(s). You should feel free to jump in here and tell us more about what would be most valuable for you to learn/better understand. My guess is that in the post college world you will come up with plenty of ideas on your own but that as an engineer you will also often be taking inputs from lots of other people and trying to turn those inputs into detailed designs.