This came to me while I was doing some cleaning. What if Kyubei itself was once human and became what it is now through a witch's curse?
The scenario would go like this:
1) Human!Kyubei, for whatever reason, makes a wish to a Witch, perhaps one that's particularly powerful, to be as powerful as she is, without knowing the latter's true nature.
2) The Witch grants the wish but does it through a curse. Since being human = no special magical powers, in the reasoning of the curse, the only way to grant Kyubei's wish is to transform her/him into something that has the powers s/he so desires. And voila! Kyubei, to its dismay, becomes the cute and creepy little beast we now so know and detest. The good news is that, yes, it now possesses the great power it has desired. The bad news, on the other hand, is that it is denied the right to use its own powers as it wishes. Kyubei, though marvellously omnipotent, is restricted to granting any one wish for every willing party. Other than that, it is now just another small, vulnerable and rather suspicious-looking animal (the subjective invisibility it enjoys could be a "bonus" attached to the curse, perhaps to prevent it from seeking help. Or it could have been a result of tricking a previous Puella Maga into using her wish for this purpose. Personally, I think the latter is more possible).
3) The Witch departs, Ohohoho-like, leaving the newly cursed little animal in a state of shock, outrage and growing despair. Determined to free itself from the curse, Kyubei seeks out anyone who would be so kind as to waste his/her wish to restore it back to normal... Only to find out that, the Witch, being meticulous, has also made it so that this method of wishing the curse away is not going to work, AT ALL.
4) Left with what seems to be utter despair, Kyubei decides that the only way out is to kill the Witch responsible, in the hope that the curse will be broken with her death. Unfortunately for it, the Witch, as we have mentioned, is a meticulous person(?) who took care not to show her real form to her unwitting victim. So while Kyubei can sense Witches, it doesn't know which Witch is the one it needs dead. And in the very first place, how is it, just a small animal, going to kill a Witch as powerful as she is?
5) So in the end, Kyubei comes to the conclusion of using the guilible as its tools. Dangling the wish offer, it fishes in anyone that bites the bait, equips her with magic and sends her out to do battle on the Witches, hoping that with luck, its unwitting minions will strike the jackpot. And these, would be the Puella Maga.
6) As the battles wear on, Kyubei is confronted with the growing understanding of the power of its enemy. While the Witches met, fought and perhaps quelled were seldom small fry, their powers pale in comparison to the One Witch that it is searching for. This introduces the increasingly urgent need to find and create a Puella Maga that could rival, no, best the One Witch in battle.
7) And finally after a long search and many lives sacrificed to its cause, Kyubei found its greatest pawn in the game. An ordinary teenager named Kaname Madoka.
.....
Now if anyone, after reading this, calls out, "WHAT IS THIS BULLSHIT?!?!?!"... Well, I guess you're not too off the mark
. As of now, I have very little (as in, no) proof to support my speculation. But this is what I do think is possible, though even imho it does seem pretty cliched.