This is what good product designers ought to be able to do - their knowledge and experience with product design (in similar or related product lines) should give them the chops to do a good estimate of production costs, etc.
So, some thoughts:
- Hire the internal expertise you need to make this happen.
- After signing an NDA with a competent design-house/manufacturer, get them to provide the details - this is their business! Expect to pay fees for this.
- Look at a similar [type of] product to get a "reasonably close" estimate. Take it apart and see what is inside or what it might take to get it produced in the quantities you want - get pricing for the components from possible suppliers.
- Make one unit yourself - buy the components and materials from potential suppliers - and see what your cost turns out to be. The low volume means that you will have a high estimate, but ... should give you guidance.
Remember to have a good set of requirements for the person or firm estimator - typically, cost over-runs occur due to inadequate specification of all the requirements up-front, or changes after you make the prototype, etc. Make sure the design house understand the product features and requirements you have in mind - in full detail.
And, of course, plan for errors in the estimate if you decide to go to production. Build in a fudge factor - using your judgement of the competency of the person or design house making the production cost estimate.
Finally, remember that creating a decent estimate for a bill of materials and manufacturing costs, will strongly depend on the volume. Here is where a competent manufacturing company will to provide a range of estimates based on how many you think you will produce.
There will usually be some minimums. So, a "one-off" product (or prototype) is likely to be incredibly expensive - the design time, cost of components, etc., - are not a good gauge of what it will cost in higher volume.