"And, while with silent, lifting mind I’ve trod
The high untrespassed sanctity of space,
Put out my hand, and touched the face of God."
John G. Magee - High Flight
There are many reasons for going into space. There's the whole "our world is gonna die, we gotta get off" theme. And there's the "next frontier" theme that is especially popular in the US right now (although it's the bad effects of "manifest destiny" that bother me about that). There's the "national pride" theme that is spurring China, Japan, and India (and to be fair, it's what drove us originally into space, we had to beat those damn Ruskies). And then there's the "scientific exploration" which is also big with the geek set (being one of them, I think I can vouch for it, after all, it's the whole premise Star Trek is set around).
All of these show up in SF at one time or another. Just like you can read the meta information of horror movies and re-engineer the zeitgeist of the society that created them (mostly American, the change of the "threat from without" and the "threat from within", how vampirism is now a viral disease instead of a moral state, the resurgence of zombies, etc). This doesn't mean they are the only reasons to go into space.
Lately there's also been an undercurrent of religiosity in SF writing (what is religion, how does it affect us, what does religion mean in a future society, etc).
So, how about an alien species making first contact with the Earth for a completely different reason. It's a gnostic philosophy that God is divorced from his creation. That he/she/it can't interact directly or interfere in the happenings of the beings they gave life to (which is also a Taoist philosophy). What if an alien species has gone into space looking for their god? The whole point of their exploration is to find him/her/it. How would that change our interaction with them, the sandbox conversations that must go on as they scrutinize us to see if we hold their God within us? And if they find that we don't hold the key (or do we), how does that change our interaction?
There are knee jerk reactions to all of those answers. You could play the current conflict (or, I should say, the oversimplification that some people like to make of it) as a template, the conquistadors, the crusaders, the Aryan (the real ones) invasion of India, the Greek state, the Mongol state, there's literally a few dozen of templates to use. But I think the deeper you think about it you'll come up with different answers.