Ok, so my theory may sound odd at first, so I will have the explanation first then the theory.
Alright: First born sun. Not first born son, first born sun. A lot of people love to think solaire or even andre, which has it's merit for andre in particular (considering he was originally slated to be the first born) but that turned out not to be the case. Now, you are given these 3 particular clues:
1.) The statues in anor londo: There is not a single one for the first born. Why is that? There is one for everybody except the first born (and maybe gwyndolin).
2.) The undead prophecy: The undead were stated to have the power to overthrow lord gwyn in order to start a new age or continue the same one, so would it be possible that the child became undead, and for fear of being overthrown, gwyn sent that child to the asylum?
3.) Gwyndolin: Think about this: gwyndolin was born male, but because of some dumb reason (the whole moon thing) was raised as a female. So knowing that the sun (not son) spelling is in effect, that would mean it is entirely possible the first born is female as well.
...Have you figured out my theory? If no one else in the game is the first born (assuming they are in the game at all) the only logical choice in my mind...is you, the player. Think about it: why is it you are the only undead able to make it this far? How come you have so much power? How come you can do the things you do and even beat gwyn? My theory is that at one point you became an undead, so gwyn (your father) feared your rise in power, so he banishes you to the asylum. Who knows how long you have been in the asylum, and who knows why...one thing is for sure, it has it's heir about it that makes me think that we are the first born regardless of gender.
Of course, just my theory.