You can also use the internet to source this type of service. You might even be able to connect with a company or companies in other countries, such as China, that can build a prototype for you. The advantage here is to be able to plan out the cost of the design and materials process with an eye to perhaps outsourcing a final build to a firm overseas.
You're right to focus on the costs to build as part of your plan but be aware that you'll likely get a lower cost by outsourcing overseas than you might be able to get locally. But you can also use the cost information (once you get it) to go to local or domestic manufacturers to see if they can match or beat overseas pricing.
They might match or beat the price, or you may be able to strike a deal with a fee once you start selling your device. Make sure it is in the form of a fee and not an ownership percentage of your company. You'll be better served in the long run with that type of arrangement.
Related: Creating a Product Prototype
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