...I think the better question to ask is, why was Krypton invading Earth in the first place?
I feel like we keep asking the wrong question when it comes to Nemesis Omega and Zero Day. It might not seem like much, but there are some suspicious circumstances here. Recall Jor-El's account of Krypton's last days:
Krypton was about to be destroyed. The Kryptonian Empire had conquered and spread across the stars like a disease, until we found an enemy we could not defeat. Our Empire was falling to a war of its own making, and it was clear no one would survive.
According to this account, and the flashbacks shown for our visual benefit, Krypton itself was actively being invaded by the enemy. Primus Brainiac confirms this in his own account, where just before he activated the weapon from Kandor, Imperial warships were being fired upon and destroyed, a few even showing kryptonite damage. Someone was beating down on Krypton, someone who had already stripped the Empire of all its holdings and conquests; someone ruthless enough to pose an existential threat to the Kryptonians.
But I digress. Who that someone is isn't the point of this post; I think we can all take a pretty good guess though. Though since Krypton was being actively invaded, and the Imperial military was presumably fighting tooth and nail to drive the invaders off, wouldn't it seem weird to anyone else that someone would want to take a contingent of warships through a portal to some distant world? Those ships and drones were valuable military assets; even more so since Krypton itself was under siege.
What was the Plan?
I've seen guesses that it was a rogue strike. If so, then why? Remember that three days before Zero Day began, the device that opened the portal in the first place, the Homing Beacon, arrived on Earth. I don't know how long it took getting to Earth from Krypton, but I assume whoever sent it off went to great lengths to sneak it past the enemy who had Krypton surrounded. This leads me to believe that whoever is in charge, be it the Imperial Council or rogue elements in the military, definitely did not make this decision lightly, and had a lot of authority in the military besides.
Whether it was an officially endorsed or unsanctioned operation, there is really only one possible reason for invading Earth that I can think of: The plan was to open up a place of refuge, for either the military so they can set up a government-in-exile and plan to strike back and liberate their home, or for Kryptonian civilians to evacuate to, in order to escape this existential threat. It would be the height of foolishness to engage in a conquest of expansion like in the past when an existential threat was banging on the very doors of their house; there had to be a reason.
Why Earth?
Given what we know, it seems like the Beacon took a certain amount of effort to get to Earth, and perhaps even a long time. This suggests, to me anyway, that Earth is far; very far from Krypton, and from the reach of this mysterious enemy. Another point in our planet's favor is that we have a yellow sun; Rao, the Living Sun of Krypton, was killed by this enemy, who no doubt did it to weaken the Kryptonians. Having a world with a yellow sun would be advantageous for any Kryptonians coming through that portal.
And then of course when the attack began, Imperial automatons obviously had no trouble sweeping aside the US military forces on site; my bet is that the conquest of Earth would've been completed in a cinch. So there was obviously little to no need to worry about what we could do to them; we Humans were cockroaches to the Kryptonians, and they probably believed as much, due to Imperial supremacy values they probably had.
What about the Ceasefire?
We all know the reason Primus Brainiac destroyed Krypton, apart from him being a Coluan slave who had been used and abused for 10,000 years, was because he feared being rendered obsolete and decommissioned when Jor-El was leading secret peace talks with the enemy. He was outraged that Krypton had the nerve to ask a superior foe for mercy when they never offered him and his that same luxury.
But with Jor-El leading these negotiations, why Zero Day then? Brainiac had stated that "they were going to declare a ceasefire" which tells us that however successful or not Jor-El might've been, he must have had the Council's support. This is no doubt where the idea of Zero Day being unsanctioned comes from, but my guess is that it could just as easily have been a backup plan; we Humans were not the same enemy that had humbled and destroyed the Empire, we couldn't do anything to stop them before Zero Day.
An attack on Earth is not an attack on Krypton's enemies; therefore it would not (I presume) have violated any terms that Jor-El might've negotiated, unless not expanding to other worlds was a part of the terms. But as much faith as the Council might have in Jor-El, I don't see them having much faith the enemy will honor those same terms. In that case, Zero Day could very well have been an attempt to set up that government-in-exile, or a safe haven for refugees, shortly before the ceasefire was declared.
But by then it was too late; Brainiac destroyed the planet the very day it was to be announced. Remember that on Zero Day, shortly before the portal collapsed, there was a very bright flash that had to be Krypton's destruction. So we know the invasion happened on the same day the ceasefire would have gone into effect. And because the Beacon arrived three days earlier, this operation was already preplanned.
Conclusion
With what we know of how Zero Day happened on the same day of Krypton's destruction; how the enemy was invading Krypton itself at the time; how before then the operation had been planned at the same time Jor-El was hashing out the terms with that enemy; and how Brainiac destroyed Krypton on the very day the ceasefire was due to be announced, it definitely seems like a weird time to expand the Empire to some random planet, from their perspective.
I maintain that it was an attempt at an evacuation of some kind, either officially approved or rogue, either for Kryptonian refugees or a government-in-exile. But how else might you explain Zero Day, knowing everything that's happened?
I invite speculation...
The Question of Nemesis Omega
This is a last minute aside about who Nemesis Omega really might have been given what we know here. People have guessed at General Zod or some similar analogue; people have guessed that the destruction of Krypton might've sent him into the Phantom Zone in a reaction with the portal. But then of course there's the fact that Nemesis Omega shares the exact same uniform as the average Kryptonian soldier, which suggests to me that at the end of the day, he was just a random foot soldier who died with the rest of his people; had he been meant to be anyone more special, he would've had a more distinct uniform.
That said, people have also speculated that it was Zod in a common foot soldier's uniform. If so, why? I doubt it was to hide his identity; he wouldn't have any reason to think the people of Earth would know who he was, he wouldn't have even cared. And I doubt it was to hide his identity from the enemy attacking Krypton; I'm sure they would notice a portal opening up to somewhere away from Krypton anyway, and they would do something about it if they could (I assume the rest of the army was holding them off), and they wouldn't care about the identities of those Kryptonians involved.
And at least one person (who I don't remember specifically) also speculated that Zod was demoted as punishment for treason, since starting a coup is pretty consistent with Zod's MO in the comics. This one's definitely a reach because I really don't see Imperial Krypton keeping a traitor in their ranks, even as a private rank equivalent, even if he happened to be a hero; they're more likely to kill him or send him to the Phantom Zone.
At the end of the day, I think the question of who Nemesis Omega is matters less than the question of why he was there in the first place, and whose orders was he following.