In South Carolina, we don't register trailers, so the fact that it is not registered or titled is normal here. It doesn't mean that it was home made. It could be made by any major trailer maker and would not be registered.
A very rare few actually will register their trailers, but only because they haul out of state regularly and other states require registration or will give you a fine even if your home state does not require it. Then you have to pay annual taxes and get a license plate for it. That's why nobody does it. I only know one person that has one of his trailers registered. He had to go back to the maker that he originally purchased from (Pace), to get a certificate of origin so he could register the trailer. People in SC buy and sell trailers here all the time with no certificates, bills of sale, or registrations. I don't have any title or any such document on my tandem axle trailer eith
The question is, can you get a document to register it in your state having bought it out of state. Does NC require registration? I'd call your DMV to see what is required and see if you can get some documentation from the seller that allows you to do what you need to do to be in compliance in NC.