Welcome to the addiction!
Regarding your basic idea:
Turning it the other way round and playing an Alien in the midsts or aftermath of an invasion poses several problems, which can be overcome.
The player has to like his character and be motivated so the alien should not actually want to kill humans. Otherwise only real weirdos would enjoy playing this.
The solution is to have the Alien on a mission beneficial for earth.
He could simply be a traitor hunted by his own kind but still attacked by humans.
It could be a challenging play not to be allowed to kill any encountered humans (scripted to loose the game in case the player does) and still having to reach a certain goal.
Or the whole invasion can be more than it appears. Maybe earth is under the threat of a genocide attack from one alien race while the other is trying to reinforce earths defenses so not to loose a future ally. The "good alien" could even be cooperating with the earth government to hunt the "bad aliens" who allready have infiltrated key positions in human society.
It could be a fun experience to play a character who can jump higher and run faster than the average human and has superhero-like fights with the aliens in an urban environment.
Or it could have been no invasion at all, but simply an accident and/or misunderstanding and the "good alien" who is the last surviving crew member has to find the hidden wreck (Area 51 anybody?)and deactivate the emergency beacon before his own kind will brutally retaliate. This would rather work as a stealth game and the alien could use "stun guns" (easily done)
so the player is not actually killing any humans.
Theses are just some run-of the mill basic plots that have allready seen movies, comic books and other games - but they do work.
In case you find my grammar and spelling weird ---> native German speaker ^^