How do I get started on building a physical non-tech product prototype?

As others suggested either try to find local crafters or build it yourself.

Is it made of leather/fabric... find someone who works this material and try to come up with a prototype.

This will let you iterate fast to modify the design/materials until you feel its the right product.
THEN you can jump into getting a "real" factory prototype or event samples of the final product for a test run, but going this way to soon will make your process inefficient, slow and expensive.

I would recommend researching product sourcing companies. They can help you find manufacturers, ensure they are reputable, help with the design, prototype, and quality control.
I have not done much research on this area myself. I read about a recent YC company working in this space: (https://www.sourcify.com/). I can't vouch for them as I have not worked with them myself, but it might help you get started with your research.

Of course, you can always head over to https://www.alibaba.com or even https://www.made-in-china.com/ and start a search there. Beware of scams though!

Upwork or find a local 3D printer

Great suggestions in the comments here. I wold also try searching on Etsy for sellers creating similar products, and to see if they'd be able to help.

You always can make it yourself, no matter how fancy it looks, it just should prove your idea.