(There's a more recent variant where the aliens are also capitalists and just buy everything up, but it's also not as simple as that.)
Looking at the history of colonisation, I think the big mistake is to conceive of humans and aliens as monoliths. This was never the case in the various colonial ventures - disasters - in our world. European colonisers did not act as a bloc, nor did indigenous peoples. Conflicts and alliances happened in all kinds of configurations, intermixing happened as well as strict separation, displacement or subjugation.
Historical developments beyond the lands being colonised mattered: The Portuguese circumnavigating Africa to bypass Muslim and Venetian traders to access goods from Asia, where they found regional interests and tensions between Hindus and Muslims they soon inserted themselves into. Religious unrest fuelling migration. Europe's taste for sugar driving slavery.
And so when the aliens arrive, what if it's a whole collection from different nations, different groups with different goals - and who's going to deal with them? The United Nations? What if the aliens just nod through the fancy UN welcoming ceremony and then go off and make their own separate deals with whoever suits them? They're not invading, they're just... pursuing their interests, driven by concerns far away from Earth.
Then the People's Republic of China buys a hundred fully autonomous semi-sentient alien war-drones in exchange for 20 tons of ruthenium. They're happy because this ensures their safety, the war-drones being capable of intercepting anything from a tank to a destroyer to an ICBM. They can cut defence spending and build more roads and hospitals! Everyone else is unhappy because their safety has just been compromised. The US buys two hundred of the same drones in exchange for Lake Superior. Canada would like to protest but is still in negotiations with some other aliens to lease them Greater Sudbury as a special economic zone.
Everyone else starts scrambling for ruthenium and fresh water, and oh, the aliens will also accept Monets but not Manets for some reason. An alien investment AI purchases a controlling share of Glencore. Electronics production collapses until we figure out how to do without ruthenium. Taiwan leases Taroko National Park to some aliens for them to build a spaceport and SEZ, with a guarantee of territorial integrity thrown in, and we are off.
The revanchist Canadian invasion of the US stalls at 47.7 degrees latitude because the licencing on the leased alien warbots only covers the area north of that line, and a low-level border war continues to simmer for decades. Attempts by the EU to negotiate as a bloc collapse when it turns out that multiple member governments are pursuing separate negotiations. The EU functionally collapses soon after. France re-incorporates a number of its former colonies in the interests of peace, stability and ruthenium deposits. It soon discovers that some aliens will sell war bots to anyone, in exchange for large enough quantities of animals - any animals.
An alien designer drug that allows humans to form highly vivid and precise memories - originally created as a learning aid - becomes popular across the world. People use it to remember their holidays, the birth of their children, fancy dates, last visits with dying loved ones. At first, governments merely balk at the degree to which this upsets their trade balance. Then people discover that if they take the drug while remembering a drug-memory, it becomes even more vivid and emotionally charged. Millions spiral away into their memories and authorities desperately try to ban the drug, but the aliens point at the free trade clauses in their agreements and make noises about penalties and alternate avenues of enforcement.
A blight starts spreading out from Mexico City. It kills all flowering plants and leaves famine in its wake.
Alien adventurers steal the great pyramid of Giza, making excuses that they thought it was an interesting natural geological formation that was just sort of lying around before escaping into hyperspace. Russia uses expensive alien technology to build a permanent base on the moon before realising that the moon is, well, barren, and no one cares. Protesters storm the Colchester Alien SEZ and set off the subjugation of mainland Britain, its new puppet government in a constant war of words with the British government-in-exile on the Isle of Man. (The Belfast SEZ kicked them out.) A project to green the Sahara with specially engineered alien plants that provide sustenance and electrical power is a bit too successful.
Aliens land in the desert of Inner Mongolia and start building vast cities without any human permission. It would be geopolitically unwise for China to challenge this, though, and so they sign a treaty ceding Inner Mongolia in exchange for guarantees of territorial sovereignity that had already been established in an earlier treaty.
Phnom Penh is conquered by a small alien force supported by native auxillaries from Vietnam and Laos. The stated aim is to oust another group of aliens that are ideological enemies, but the troops never leave. Soon after, Peru and Bolivia go to war over the same ideological difference, meaningless to humans, but all-important to the alien forces that their governments now depend on. The warbots they use have no concept of combatant versus civilian, and so the human casualties are enormeous. Exactly three aliens lose their lives.
There is no overall plan. There is plenty of blame to go around, but there is no grand scheme to conquer and humiliate and impoverish Earth. There doesn't have to be for it to happen.