The giant arrives on Earth with what looks like a meteor impact responsible for its amnesia. If it was such an impact, it might not even be on the planet its creators intended to launch it at.
When Hogarth and the Giant go out walking at night, pay attention to the moon in one scene. Just to the right of it, one of the stars can be seen moving. That's Sputnik.
A deleted scene more heavily implies that that is, in fact, what happened.
Dean and Mansley both represent a respective positive and negative viewpoint of how trusting people were in the Fifties, particularly when it came to children:
Dean is a counter-cultural Beatnik who could potentially be a bad influence to Hogarth and when the kid turns up in his scrapyard late at night, he promises not to tell anyone, which would definitely raise eyebrows these days. But Hogarth takes an instant liking to the guy and when it's revealed to Annie that her son sneaks out to play at the scrapyard, she seems unquestioningly okay with it. Their trust is ultimately rewarded when Dean puts Hogath's safety at top priority and becomes his stepfather in the end.
Mansley on the other hand is a professional man who works for the government and even though Hogarth immediately despises the man, Annie has no reason to worry about her son's safety even suggesting that he take the stranger on a tour around town. Her trust is ultimately misplaced when Mansley treats Hogarth with increasing hostility going so far as to lie to General Rogard about the Giant killing a kid to provoke a military strike when he knows damn well that the boy is in the crossfire.
Why does Mansley keep using nicknames for Hogarth instead of his real name while pestering Hogarth? Because he thought the name was too stupid for words and is now refusing to use it.
As mentioned under "Foreshadowing," the Giant grouching about having to play as Atomo, instead deciding to play Superman, when he and Hogarth are playing in the junk yard, sums up the entire ending of the movie: he rejects his assigned role of "a big gun that walks" and becomes the hero that he chooses to be.
Major Spoiler The Giant wasn't destroyed because the nuclear bomb didn't explode. To be specific; there was an explosion, but that came from the impact. The explosions of Nuclear weapons are the result of a precise detonation process, they don't detonate on impact. Impacts to the missile are more than likely to ruin the entire trigger mechanism. Since the Giant purposefully impacted the missile, there was a lesser conventional explosion from the components of the missile that knocked him apart like the train.
While Hogarth certainly broke the eight o'clock bedtime and Annie's "no late snacks" rule, he could have been interpreted as using Loophole Abuse for her "no scary movies" rule, since while it was a horror movie, it was a bad B-movie and he didn't seem scared of it at all.
The gigantic robotic super weapon had to come from somewhere (which the movie never acknowledges). It's likely that those who sent the Iron Giant to earth are not going to just give up after one failed attempt. This deleted scene shows the Iron Giant's memory of him and an army of others of his kind destroying another planet. The fact that the creators were so willing to sacrifice an army of them also strongly hints that there are plenty more of them, too. Also, the end of the movie explicitly shows us that the robots can survive nuclear blasts. And who's to say that he's still friendly after reassembling himself?
The very last image of the film is him giving a friendly smile to the camera. We're fine.
Nothing about the dream or the machine's armaments suggest anything other than that it was sent to destroy planets regardless of inhabitants and that it would use those weapons if anyone tried to stop it. The kid's really lucky that it suffered the damage that scrambled its programming.
As fridge brilliance points out above, the Giant's landing on Earth definitely wasn't intended. It landed hard enough to damage its memory, and unlike in the dream Earth only has one giant arriving, not an army of them. So Earth at least wasn't deliberately targeted by whatever made the Giant. That does leave the fridge horror of whether the Giant's creators might still deliberately target Earth at some point anyway, given it's completely unknown what their motives are for deploying planet-destroying mechanical armies (but it'd be a safe bet the motive isn't a very friendly one).
All those threats Mansley made against Hogarth while trying to get him to reveal the Giant's location? Despite Hogarth's protest, he probably could do all of them considering Annie's vulnerable position and single parent status.
And imagine how much easier it would have been to carry out said threats if Hogarth wasn't an only child!
Single parent wouldn't even have to enter into it. This was the Cold War, then the US government was more than willing to smear someone as a communist in order to get what they wanted. Which is a whole new level of horror, because all of Mansley's threats could have easily been carried out under "national security".
While deserved to the point of probably fitting more in the Fridge Brilliance section; depending on your point of view, Mansley might've been more than just incarcerated for his actions when the general arrested him. He committed crimes against his own country in his crusade to kill the Giant (nearly bombing an entire town and fleeing in the face of duty). Given the General wanted to have Mansley die along with the town when the missile hit, he likely had Mansley executed during the time skip at the end.
In the battle sequence near the end of the film, the Giant's seen blowing up, shooting holes in and deleting from existence several M41 Bulldog tanks. In each case the animators make sure to show the crews bailing out before the tanks themselves are destroyed. The thing is, the M41 had a crew of four, yet we only see two people escaping from the tanks. This could just be sloppy research on the part of the writers, but if not. . .
Note that this film is set at the height of the Cold War, and Mansley and General Rogard think (albeit before the Giant goes berserk and reveals the extent of his weaponry) that the Giant was sent to the U.S. by Russia or another foreign human power, and there's nothing for the rest of the film to explicitly confirm that they realized the Giant was extraterrestrial in origin. Despite the upbeat ending with the Giant being rightfully regarded and remembered as a hero for his actions, in the bigger picture; it's possible the Rockwell incident could've heightened Cold War tensions within the film's Alternate History if the politicians and military leaders never realized the Giant was alien in origin, since it'd be obvious from the Giant's weaponry array that he's an Anti-Anti-Christ by origin. Bare in mind, looking at the Cold War's history will tell you there were a few points in the Cold War including the 60s' Cuban Missile Crisis where we passed within inches of having World War III and were mostly only saved by minute decisions and chances.
On the bright side, if the politicians and government figures are reasonable enough to realize that the Giant is alien in origin and might've been deliberately sent to Earth as part of an Alien Invasion before he went I Am Not a Gun, it could actually act as a Conflict Killer, causing Cold War tensions to decrease in the face of a possible greater enemy from the stars who's even more technologically advanced having potentially turned their attention to Earth.
Speaking of Russia... The first thing they'll know will be that the US deployed a lieutenant general and a large Army/Navy combined force, including a battleship, to a small coastal town, and they then detonated a nuke above it, high enough it didn't destroy the place. What will they think about it? Especially when the US admits there was a giant robot of unknown origin...
The Giant grows to abhor killing over the film, with his first introduction to it being the killing of a deer by hunters which leaves him shocked and dismayed afterwards. How would the Giant react if he found out about humans eating farmed or hunted meat, and how commonplace and socially-acceptable it is among bad and good humans? Also bear in mind, Annie's mention of cold chicken in the ice-box indicates she and Hogarth aren't vegetarians. This is a Fridge Horror point you could probably apply to quite a few other stories, but it's a valid point considering how the Giant reacted to the deer's death.
We humans give our troops the bare minimum necessary to complete the task they're assigned based upon how much it costs to run a military. Our guys get M1 Tanks, F-35s and Nimitz Class Carriers because that's the minimum things necessary for the US military to do it's job. This "minimum necessary" doctrine should theoretically apply to aliens too, and if the Giant's armed as it is, and there's hundreds of them available, just what the hell was it built to fight against?
The giant fires a Wave-Motion Gun meant for a battleship out into the ocean. Any other ships in the blast radius would have been vaporized.
In addition to being an unstoppable war machine, the Giant shows us at the very end that it can recover from being blown to hell. So imagine if it was still in battle mode and got scrapped? It may take months, may take years, but it will self-repair and resume its mission eventually.
shows the Iron Giant's memory of him and an army of others of his kind destroying another planet. The fact that the creators were so willing to sacrifice an army of them also strongly hints that there are plenty more of them, too. Also, the end of the movie explicitly shows us that the robots can survive nuclear blasts. And who's to say that he's still friendly after reassembling himself?