Generally speaking, if you are not a prohibited person and you live in a location where it isn't against the law to manufacture or posses it, there is no federal law preventing you from making a firearm for personal use.Can be done, yes, and as soon as it is caught, the person can, and probably will, be prosecuted for manufacturing firearms without a permit, which is a sentence of 20-40 years in federal prison.
A semi-talented machine smith can manufacturer an AR upper receiver in a matter of half an hour from a block of aluminum, too. There is no avoid this aspect, with any gun. With a CnC machine, I could make an entire custom firearm. With simply a metal pipe and a pin, anyone with average intelligence could make a .22 firearm that would shoot. (A pop-gun) The same laws apply, though. Manufacturing a firearm without a license is a federally mandated minimum of 20 years in prison. If found to be done to specifically avoid background checks, it can be considered "egregious" and could end up with a sentence of up to 40 years.
No background check is required. Most states you don't even have to serialize it or register it.
https://www.atf.gov/firearms/qa/does-individual-need-license-make-firearm-personal-use