I've been thinking of a scenario in which the US wants to control the entire world, via time travel, but I'm not sure what time to travel to.
The US is generally considered to have the most powerful military in the world today, but it could certainly not stand up to every other country at once. However, if the same military were to appear in 100 BC they could easily do so, due to their advanced technology (planes, machine guns, etc).
The idea is that the entire modern USA and what is in it would be transported directly onto it's geographical location in the past. This would "overwrite" anything else currently there, AKA the Native Americans.
For various reasons, the population of the US is highly supportive of this war, like they were in 1943. Therefore there is no worry of internal revolt. Industries are also geared towards helping the war effort. The government has been planning this for 10 years, so they have stockpiled lots of ammo, materials, fuel, etc. Assume their technology is modern with the exception of the (one-use) time machine.
The goal is to conquer every nation in existence at that time. I'll consider nations to be political units with more than 50,000 people. I consider "conquered" to mean "an American in their capital, with the authority to make and enforce laws". If there is a better criteria for either of these let me know. I think it would be best if this goal was accomplished within 20 years.
The US won't be evil, and would eventually let the people become normal citizens after their previous government is destroyed. However, the nations it is conquering will presumably resist at first. After the war gets going, the other nations will band together against the US like they did against Germany in WW2, so we would need to fight off everybody at once.
So: How far back would they need to go?
I would guess they would travel to sometime between 1500 and 1800 AD but I don't know enough specific history to get closer. I'm looking for the time in which it would be likely to succeed, given realistic events.
Edit I see a few answers stating that any time before 1949 would work, due to nukes. I would like to clarify that the US still wants the countries to be livable and usable, so nukes would prevent this. Also, for a story that's not very interesting. So please don't involve nuclear weapons anywhere in an answer. Sorry for the change, I honestly forgot about nukes when writing this.
The time travel works in an alternate-universe / alternate-timeline way. So the modern US drops all past "dependencies" when it is transported to the (alternate) past. There aren't any paradoxes with who made the US, it makes a new timeline.