Just an honest, open question. I have an idea of like to have for a hat. However, knowing how to go about getting the correct file formats or knowing the cost of what is asked for in advance seems like a foreign language. Much less if there are design corrections back and forth. I’ve dealt with organizational offices doing similar, but never anything private. Is that even a thing?
Look for a local print or embroidery shop that you can get like work shirts and business cards and whatnot made. Unless you’re really in the middle of nowhere, there’s probably a local print shop that will at least be able to point you in the right direction. If you want a one off instead of a small batch look for a place that offers embroidery - it sounds more expensive but because they can just throw whatever on the machine and do a one off, it’s usually actually less expensive than traditional screen printing. Specifically for hats in not sure if you can get them digitally printed in most smaller local shops.
I will look around, thank you.