While there's no explicit mention of alien contact in Alien, we can make a few assumptions based on the later films that suggest that alien contact was probably already made by the time the events of Alien begin.
The Nostromo is on its way back from a mining mission on a planet around the star Epsilon Reticuli when it answers the distress call from LV-426. Epsilon Reticuli is roughly 59 light years from Sol, past what is known as the "outer rim" of inhabited space in the Alien films.
Several decades later, during the events of Aliens, this exchange takes place between two of the space marines:
Frost: Hey, I sure wouldn't mind getting some more of that Arcturian
poontang! Remember that time?
Spunkmeyer: Yeah, Frost, but the one that you had was a male!
Frost: It doesn't matter when it's Arcturian, baby!
Arcturus is around 38 light years from Sol and is in what is known as the "core systems". We can assume that Arcturians are alien indigenes of a planet orbiting Arcturus, and that humans have have made "contact" with them.
Given that Arcturus is considered a core system, and that ships were visiting areas past the outer rim and therefore considerably further away during the events of Alien, we can assume that Arcturus was visited and contact made at a time prior to the events of the film.
This would explain why no-one is mind blown at the existence of aliens, per se.
Here's a non-canon map from the Alien Anthology Wiki to give you an idea of the Alien galaxy:
And there's a discussion of the whereabouts of the Nostromo here