3D printing a prototype won’t forward your patent application. You need to speak with a patent attorney to get the steps that you will need for your specific idea. Most will do an initial consultation for free.
By the time you have a 3D printed prototype, you have developed the idea far beyond what is usually needed for a patent. You have developed 3D models and performed calculations, etc.
The process I usually suggest to my customers is:
1. Document the idea on paper with as much detail as possible, in ink, and have it witnessed. This establishes your ownership of the idea. Periodically update the documentation in the same manner. This is when you should be starting the patent process, to get at least a provisional patent to protect the idea as soon as possible.
2. Develop a CAD model. This is required to 3D print. If you are not able to develop one yourself, ensure that you have an non-disclosure agreement in place with the person/company who develops the product.
3. 3D print the prototype for further development.
4. Refine the design.
Be careful, because as soon as you speak about the idea publicly, you have one year to get it on the market or have a patent pending to protect your exclusive rights.