For our hypothetical let us imagine an eccentric billionaire that has some how managed to mine some plutonium and uranium, or whatever.
Said billionaire is inside the USA and acquired everything legally inside the USA(this is iffy) but roll with it.
When the NSA or CIA or FBI or whoever come to seize said weapon, what law will they cite?
I suspect that the drones and SEALs will show up first.
18 U.S.C. § 831 - Prohibited transactions involving nuclear materials
Additionally,
42 U.S.C. § 2073 - Domestic distribution of special nuclear material authorizes the NRC to create licensure requirements for handling of nuclear materials.
I’m pretty sure the much-vaunted Second Amendment ought to override both of those silly statutes! 
I recommend you acquire a nuclear device and make it a test case. Should make for some fascinating jurisprudence. Which you’ll have time to read in prison. 
The law of the iron fist.
The Progressive Magazine went to the public library and assembled information they found there, and published a handy DIY article about how to build a nuclear device, and somehow the US government found a “law” than even violated their First Amendment freedom of the press.
It’s the “born secret” law:
Basically, here’s the deal. The US Government can declare anything they want to be illegal, and prosecute under whatever pretext they like, and doing so will have force until a plaintiff succeeds in having a challenge to the edict sustained by a Federal Court order, and sometimes that doesn’t even stop the government.
Apparently, some kid attempting to build a nuclear reactor in his garage found out - the hard way. 
I’m not sure the OP’s hypothetical actually violates this law. It says someone is in violation if they:
If the OP’s mad millionaire has built an nuclear bomb, they have the capacity to cause death, injury and/or damage, but they haven’t actually done so, so ‘A’ doesn’t apply. ‘B’ is weird and vague, but it’s not clear to me that it applies either.
“B” applies if the government says it does, and gets a judge to agree. Or doesn’t ask a judge, and cites national security interests in keeping a judge out of it even if your hypothetical nuclear billionaire wants a judge involved.
IANAL. I just pay attention to how the law is actually applied in areas the government has a keen interest in.
They don’t get to keep the judge out of it if they are prosecuting. At worst, they could seize your homemade bomb.
OR they could have saved the time and effort and bought a copy of whichever damned SF magazine it was back in the 1970s that published an article on how to turn your 2 story, attic and basement tract house into a nuke bomb - you position one hemisphere down in the basement, and drop the other half down a tube onto it from the attic as I vaguely remember.
To be blunt about it, the only thing you need is the correct amount of fissionables to go critical, divided in half and formed into 2 hemispheres. You then need to put them together so the mass goes critical, and mother nature will do the rest.
cough Demon Core cough - the jackass was manually manipulating both halves of the core, the screwdriver slipped and the 2 halves came together, letting out a lethal [to him almost immediately] amount of radiation.
It isn’t rocket science, not even close. The amount of fissionable is known, the tricky part is in getting the fissionables in the first place. Hell, I wrote a paper on the whole deal back in high school back in the late 70s myself. The only problem with plutonium is that the rods used in nuke plants produce it as a by-product. As I remember the rods used for plutonium production are pulled out and stored after being used for a short time, rather than the normal lifespan. I have no idea of knowing if the rods I walked past on a daily basis when working as a rad whore were being used for production or not. [TBH, nor do I particularly care. Not my job to worry about them, just to repair/refit the plant.]
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Actually, it’s quite a bit more difficult to create a working bomb.
Even a gun-type U-235 bomb requires more engineering than just dropping two hemispheres together.
An implosion-type bomb design is still out of reach of many countries, so it’s not something you are going to build in your garage…
In Near v. Minnesota, 283 U.S. 697 (1931), the US Supreme Court held prior restraints to be unconstitutional, except in extremely limited circumstances such as national security issues.
One can only assume that the national security people would perk up their ears if they heard about somebody with a nuke, and have a precedent on which to act. Then, only the fuzzy broadness of “national security” comes into play.
A prior restraint is a limit on speech, not conduct.
Oddly enough, I still can’t figure out what would be the penalty for building your own atomic bomb.
They make you test it yourself.
Slow and painful death from radiation poisoning?
Ugh. People hate tests.
42 u.s.c. 2272.