But what if aliens didn't reach Earth first? What if we beat them to the punch and showed up on their world?
The aliens would almost certainly not be intelligent. They would be like any other animal, plant, or insect species from Earth. We would probably not eradicate them just for kicks, but we would try to learn how to manage them. If they taste good, we'll breed them like we do chickens or cattle. If they're plant-like, we'll plant them and prune them with aesthetic goals in mind. If they're insectoid, we'll put up mosquito nets.
But what if, against all odds, they did turn out to be intelligent? In that case, I think "first contact" would proceed just like it has on Earth. The human invaders will be greeted courteously, and will be courteous in return. Everyone will get along. The two species will become friendly. They will discuss trade possibilities. They will have Thanksgiving Dinner together.
Everyone back on Earth will hear about the success of the mission and be eager about the new opportunities. And then they will go there.
They will settle the alien world in massive waves because the aliens don't levy income taxes, or enforce speed limits, or file frivolous lawsuits, or engage in any of the other multitude of things that humans don't like about home. It will be a lawless frontier, and it will draw rugged individualists, criminals, and naive ordinary people who have no idea what they're getting into.
Over time, as more and more humans pour in, the aliens begin to see the threat. They see themselves being dispossessed of their land. They fight back. But human technology is superior. After all, we made it to their world. They didn't make it to ours. The aliens are eventually pushed to the fringes of their world.
This scenario has played out many times on Earth. There is no reason to think it wouldn't play out this way on an alien world. It's not a happy scenario. Just a human one.