So the usual way of getting 'force rating on' and access to force powers is thorugh the force sensitive exile specialization, but is it the only way?
I was thinking about letting the characters discover an ancient artifact, which make one of the characters realise he/she is a force sensitive and recieves a force rating 1. That would allow the player to purchase powers without having to buy the specialization tree right?
Sure, but the more elegant solution would be to bestow upon them FSE ilo XP. That way, they gain access to the talents and can make it to FR2 if they choose (and if they enjoy Force powers at all, they will choose.)
You can do anything you want in your game. Something I would be concerned about in your situation is that you are giving one player a force rating what are your other players getting? Unless everyone knows this part of the quest arc is designed to provide something for one player you may run into hard feelings.
To Lorne you must listen!
Giving the new FS a "free" buy in on the FSE tree and awarding all the other players XP of an equal amount to what the new FS would have spent had he bought into the tree is better and more fair.
Just handing them a loose FR 1 actually kicks the player in the nuts a little because if he wants to do more then basic force powers he's gonna have to buy into FSE, but gets no new bonus for actually doing so. Remember, buying into FSE or emergent gives you a FR of 1 unless you already had 1 or better. It does NOT grant +1FR.
So the usual way of getting 'force rating on' and access to force powers is thorugh the force sensitive exile specialization, but is it the only way?
I was thinking about letting the characters discover an ancient artifact, which make one of the characters realise he/she is a force sensitive and recieves a force rating 1. That would allow the player to purchase powers without having to buy the specialization tree right?
You do whatever works at your table to have fun.
I think what has been suggested is good, in that rewarding the force sensitive exile or emergent talent trees or xp equivalent for the one receiving it to the rest of the players. There's a host of talents that should be available to force sensitives, rather than simply having access to powers. Granting a Force Rating of 1 without a tree means that they can't improve it in any way, short of buying into a force-based talent tree. Granting a "free" FR1 in the long run isn't free, but is actually more expensive.
As others have pointed out, however, it is your table 
Good answers. Thanks:)