Indeed, nuclear weapons are a tricky thing. On one hand, there are nuclear non-proliferation treaties, on the other, peaceful nuclear power plants. To obtain nukes, you have to have good relationships with the current big powers, build peaceful nuclear installations, and very covertly produce the weapons based on it, while the big boys look the other way, or maybe even secretly help. That's approximately how China, India, Pakistan, and Israel obtained their nukes. (North Korea is a special case.)

Once you've obtained some nukes, complete with decent rockets to liv them, nobody is going to mess with you too badly, or try to take the nukes back; you're now a member if the club.

Japan or South Korea would likely be able to produce nuclear weapons in a few months if they needed to. I bet even Ukraine could, with its remaining nuclear plants and relatively advanced industry, and are on friendly terms with the US.

But if you made enemies with the big members of the nuclear club, and with the US in particular, they will do everything to stop you, and your situation would become much harder; that's the case with Iran.