Regarding the “Shall not be infringed.” part of that, I would imagine owning a firearm without a serial number has most likely been made illegal or requires massive amounts of governmental oversight and fees to possess.
If you make it for personal use, you dont need a s/n.
Firearms made before 1968 did not have to have serial numbers and are very legal to own.
There are millions of them out there and noted in another reply home made ones to not have to be serialized.
I have a late 1940s vintage Remington .22 rifle that does not have a serial number. It wasn’t required until after the Gun Control Act of 1968 was passed.
Which is why my B-I-L asked me what serial number I would like on the deer rifle he made for me out of parts and pieces lying around his shop. He abhors the ATF.