Simple answer:
Could they? No. The world was pretty big, Murica pretty much in bad shape after the war. That 'we got the bomb', there where like three nukes, Trinity, Fat Man and Little Boy. It cost the U.S. billions back then to only get those three. And then it took some years until they had a real nuclear industry up and running.
There's no way, the US could have fought the Commonwealth, USSR and pretty much evereyone else.
Should they have? Only with the intention to destroy themselves as well as the world economy.
Did the US make mistakes (much) later? Yes. One of them is far to much wars.







